We know from canon that Sherlock Holmes had French relatives; could he, perhaps, have had BELGIAN relatives? Perhaps that is why Poirot didn't go back to Belgium after the war, if he had relatives, albeit distant ones, in Britain.
Poirot is the master of psychological manipulation and he mentions in several stories that the murderer-by-proxy is the perfect killer, so he is aware of this kind of application for his psychological skills. He is also constantly bored out of his mind, until a murder comes along for him to solve. Maybe those brilliant little grey cells are manufacturing murders all around him for him to solve.
Consider a typical crime plot Poirot solves: 1. Poirot is bored out of his mind. 2. Poirot goes to a purely social event/party/holiday resort/dinner to an old friend. 3. Poirot introduces himself as the world's greatest detective to both the victim and the future murderer. 4. Poirot dislikes the future victim for some reason. 5.Murderer commits the act. 6. Poirot is on the job and no longer bored. 7. Poirot puzzles the case, not understanding some question. 8. Poirot comes up with the crucial clue and suddenly understands everything. 9. Poirot blames his little grey cells for being stupid not realising the solution sooner. 10. Poirot has his presentation and enjoys enormously taking apart everyone present with his ruthless reasoning. 11. The murderer breaks down and makes a raging confession even despite flimsy or no evidence against them, sometimes exhibiting behavior indicating completely uncharacteristic mental instability. 12. Poirot makes a satisfied comment about evil existing everywhere right under the surface.
Maybe Poirot's little grey cells are the real killer in these stories. Poirot suffers from boredom and won't use drugs to relieve himself like Sherlock Holmes does, so his subconsciousness arranges murder-by-proxies for him to solve. They give people around him all kinds of ideas, strengthening existing grievances, encouraging perfectly ordinary people throw caution and fear into the wind and act out on their dark desires and implement murder plots which may have been little more than fantasies to begin with. The little grey cells even use the opportunity to make the annoying person the primary target. Notice that almost always Poirot has a sudden moment of realisation and bemoans his own little grey cells for not figuring the crucial piece of information sooner. Maybe the little grey cells did figure it out early on, but kept it from the conscious Poirot to prolong his pleasure. Sometimes the murderer turns out to have a rather petty reason to kill the victim and on several occations had no time sensitive reason to kill the victim precisely when the risk of being caught by the world's greatest murder solver was at its highest. How many of these people would never have committed any crimes, had the Poirot's little grey cells not distilled their little grudges into murderous malice?
When Poirot is finally done exposing the murderer, his/her reaction to his speech is also quite odd. The murderers never lawyer up or protest their innocence. Instead they usually either express relief that the nightmarish play in which they have been forced to keep killing their friends and loved ones just to keep it going for a little longer is finally over and they get to be human beings again. In the TV series, when the murderer admits to the killing, he/she usually recites his/her motive for the murder, flatly, almost mechanically, like they no longer believe in their own story. It is like those motives have long since been transformed from reasons into mere excuses to keep the murderous game going a little longer. Alternatively they have a total nervous breakdown and attempt attack Poirot. Is that the behavior of an exposed criminal, or a trapped animal attacking its tormentor, the moment where the spell is broken and they realise on some level that they have been played like marionettes? Some of the murderers even babble incoherently, gone mad from having to commit murder after murder just to keep the masquerade going a little longer, their original motives completely sidelined. They never get remorseful after the murder confess their crimes. They stick to their plotting and solve all obstacles with more murders until Poirot exposes them and the game is over.
Also keep in mind that the murders happening around Poirot are all elaborate and complicated puzzle murders. There is not a single sloppy or straightforward murder whenever he is present. It is like all the murderers near him catch a sudden case of complexity addiction. How realistic is that, unless these murderers were manipulated into committing these acts in specific way to challenge Poirot intellectually?
This troper made a quick episode summary check and found 24 matches out of 70 cases (The King of Clubs, The Third Floor Flat, Triangle at Rhodes, Problem at Sea, Peril at End House, The Mysterious Affair at Styles, Wasps' Nest, The Mystery of Hunter's Lodge, Death in the Clouds, The Yellow Iris, The Underdog, The Case of the Missing Will, The Adventure of the Italian Nobleman, Dead Man's Mirror, Jewel Robbery at the Grand Metropolitan (theft, not murder), The Murder of Roger Ackroyd, Evil Under the Sun, Death on the Nile, The Hollow, The Mystery of the Blue Train, Cat Among the Pigeons, Appointment with Death, Three Act Tragedy, Cards on the Table). That is 23 more pre-murder, coincidental connections to murderers than any (innocent) person should statistically have. Usually, when a person knows more than one mutually unconnected murderer-victim pairs before the murders happens, it usually means that the person is himself somehow involved in the murders. Yet we are supposed to believe that Poirot has met 23 of these pairs without being involved in any of these cases? In each of these cases the murderer didn't even start the murder plot, until Poirot met with both the victim and the murderer. How many of these would-be murderers would never have committed any crime had Poirot never been involved? Sure many of them had a good motive and some had pressing time constraints, but not everyone with a good motive and a plot planned has the courage to follow through. Did Poirot subconsciously give them that final push?
There are also 12 partial hits (Hercule Poirot's Christmas, Hickory Dickory Dock, The Double Clue (theft, not murder), Murder on the Links, Dumb Witness, Lord Edgware Dies, Murder in Mesopotamia, Murder on the Orient Express, Dead Man's Folly, The Affair at the Victory Ball, The Mystery of the Spanish Chest, Double Sin(theft, not murder)). These are otherwise matches, but the murderer already had some kind of plot ongoing by the time Poirot got involved, but the murder itself happens after Poirot arrives and makes himself known. That amounts to 35 times that we know of in Poirot's life he went to a place on an unrelated issue and a murder (or sometimes a theft) happens there shortly after, 51% of all his cases, over half. In 33% of all his cases Poirot was present in only a social capacity, not trying to catch anyone. That is a statistically impossible string of coincidences. Something else must be going on.
Let's investigate the case in point: Appointment with Death, which this troper just finished watching. The victim in that story, Lady Boynton, is a reprehensible character everyone hates, Poirot dislikes her early on, and naturally she ends up murdered shortly. Bonus points for the murderer's motive not being time sensitive. The murderers could have waited until Poirot had left and continue unhindered. Instead the murderers knows that Poirot, the world's greatest detective is nearby, yet commits the murder anyway at that point. According to Poirot's summary the murderers had not even arrived to the area with the intention to commit the crime. The murder came into the plans after the murderers had met and talked to Poirot.
Finally let's view Poirot's last case from this angle. In Curtain Poirot himself becomes the murderer to stop Norton from continuing his spree of murder-by-proxies. How did Poirot even realise that such a killer was about? Maybe it takes one to know one. Then after killing Norton Poirot stops taking his meds as an atonement. What if he was atoning for more than one murder? Did he realise in his final moments the similarities between Norton and himself? He already decided to remove one murderer-by-proxies to protect the world so did he let himself to die for the same reason?
- The most bizarre example of this effect is in The Hollow, where the murderer is a ditz. She commits the murder and does one smart thing to cover up, but it is not enough to keep her from being caught, so the entire cast of suspects gets a sudden obsession to convolute matters further to keep Poirot off the track. Initially only one person goes along with this coverup, but the more Poirot gets involved, all the suspects join in one by one. Not a single one of them thinks that they themselves could be charged for being accessories to murder after the fact. All of these people are probably going if not to the gallows then to jail, just so Poirot could get an extra day or two puzzle solving.