Now that doesn't explain why he wanted to buy Twitter in the first place, but there doesn't necessarily need to be a strong reason. He got frustrated as a user, he got bored, he thought "hey why not buy that thing" and that set a series of cogs in motion that couldn't be stopped before it was too late.
(He's the richest guy in the world; one would assume there are armies of people around him making sure his desires are met fast. If he says "let's buy Twitter", then those people make it happen.)
I don't think he has the beginning of a plan. He said "free speech!", and then also "but not hellscape!" But, some amount of free speech without being a pure hellscape is close to what Twitter is right now. That's not a plan for the future, that's an observation of how things are at present.
If he can simply wait for Twitter to be worth as much as he paid for it, so that he can sell it again and cover his losses, that will be a fairly good outcome.
Easier said than done, though.