This might have been said before, but there's one thing I think is a bit weird, perhaps even ironic is this:
Trump's presidential platform right from the start (2016), summarised in one image was this:
He said the shit that all the bigots wanted him to say. Basically every kind of dirt that every Presidential candidate would dread came up and he must have expected this to happen, and ordinarily any one of these bits of dirt would have sunk a campaign but not his because his supporters hoped he would lead like the song he had sung to them which no-one else dared to. A dream come true.
In that setting, why bother going out of his way to keep Daniels quiet at all? Just declare it fake news and that's all his fanatics would need, which (aside from the illegal stuff) is exactly what happened. If his potential audience generally believed and took issue with just one shred of the dirt against him (or considered the sheer amount of dirt against him adding up to "where there's smoke there's fire"), he was sunk. If his affair with Daniels was the only bit of dirt then trying to keep it quiet would make sense.
I realise that this argument is easy to make in hindsight but it's also logically true. He's had multiple affairs, multiple marriages, multiple shady business practices, multiple failed businesses, multiple lawsuits, he likes to peep in girls' locker rooms, he has a very ambiguous relationship with his daughter... the list goes on.
My conclusion is that a man like Trump enjoys the use and abuse of power, so even though the hush payment to Daniels was logically unnecessary, the idea that he can control people and so get away with shit is something that satisfies his ego. On the other hand, declaring Daniels to be fake news must surely also be a similarly enjoyable abuse of power and it's not even illegal, but perhaps there's less of a kick out of it because it's legal.