Apparently it's a very obscure visual pun. If you read the Japanese word for "apple", "ringo" with Chinese conventions, it becomes "pingu", which is also why the penguins are called "pingu", rather than the more conventional "pingin". And the apple is ofcourse the most important symbol in the series — the apple cut in half is the eponymous "Penguindrum".
It does relate to the plot as well if you think about it. Sanetoshi and Kenzan first met while on an arctic trip, and that is where they decided to form Pingroup. Likely, they made their symbol a penguin in reference to the way it began. Then the Princess of the Crystal took over Pingroup after they changed their name to Kiga Group. As for why she chose to continue the penguin theme we can't be sure, but at least it works thematically.
So what purpose did Mario ultimately serve? The big revelation of him owning another penguin hat, and thus the other half of Momoka's soul ended up meaning exactly squat in the end.
Wasn't Mario meant as a trigger for Masako to join the hunt for the Penguindrum, just like Himari triggered Shouma and Kanba to search for it? Episode 16 was pretty explicit about that; Masako agreed to hunt for it in order to save Mario's life.
And to follow up from that, what was the Princess of the Crystal, in the end? We see that both Momoka and Himari are distict entities from her, and neither has a personality like her's, so what is she and why did she come into being from their union?
The Princess of the Crystal was one-half of the containers that sealed Momoka away, in the same way that the two bunnies/twins were the two halves of the container that sealed Sanetoshi. If the bunnies are any indication, the personalities of the containers are distinct from, but supportive of, those who they are sealing. As for why the penguin hat needs to be placed on someone's head for the Princess in the Crystal to take over, and the bunnies don't, though...
I think the reason you need to wear the hat for it to work is because that is how someone would normally use a hat. There were several times where Sanetoshi was visibly feeding the two bunnies carrots or treating them as mere pets. This could be the reason the bunnies do not have the same restrictions as the Princess of the Crystal does, as they are functioning like any kind of pet bunny would.