As anyone who's ever actually read his stuff could tell you, Pr. Lewis was not a foolish man. All the dumb issues that come with the You Have Failed Me trope would doubtlessly be plain as day to a man like him. But as he makes clear in other works, the demons reject God and all their works, but God is the Father of all things, including basic logic. So of course they'd use such dumb and counterproductive tactics as this trope!
In "Screwtape Proposes A Toast", Screwtape justifies seeking to damn people for minor sins on the grounds that it's Boring, but Practical; the resulting souls may not be as enjoyable to eat as truly great, passionate sinners, but they are much less risky to acquire. However, there might also be another reason for using this strategy, when you consider that Lewis portrays demons as pretending to be allied while actually all seeking to ruin each other. Keeping up a steady supply of subpar souls means you get to be just helpful enough to avoid getting fired, but without doing something as un-demon-like as making another being happy.
One about the lack of good sequels...part of it is that while most tend to use it to speak about elements of society that they dislike, they forget that one of Lewis' best sources was his own PERSONAL temptations. Lewis loved Britain, and spoke about its flaws from that perspective, where most evangelicals see themselves apart from society.
Overlapping with Fridge Brilliance. Throughout the letters, Screwtape keeps addressing Wormwood as "my dear Wormwood" and referring to himself as "your affectionate uncle." As the letters progress, we find that devils never feel love, and indeed don't even understand the concept. Then, in the final letter, we find that Screwtape gets particularly affectionate towards Wormwood as he prepares to eat him. His "affection" (reciprocated, apparently) was hunger, and his terms of endearment were Terms of Endangerment all along.
The sheer power the devils have over human thoughts is terrifying, as again and again Screwtape has Wormwood influence what the Patient thinks and feels, and whenever he gets wise to it winds up with his good thoughts corrupted (such as becoming proud of his humility and otherwise thinking he has seen through the devils traps), such that even someone who believes he is coming closer to God and shunning the Devil may be merely playing into Satans hands all along and end up in Hell, and there is nothing he can do about it.