The only remotely plausible explanation that isn't plain narcissism on Elon's part is the hypothesis I found on Matt Levine's blog (which he credited to someone I forget): Elon, by positioning himself as a conservative, hopes to convince Republicans to buy Teslas (and his other products).
There are a variety of problems with that approach — not least that he'd be aiming for the primary targets of oil company propaganda.
Alternative possibility (which, to clarify, is just a random idea of mine, not even a hunch): he sees himself as some sort of political figure, either as a candidate or as a kingmaker – just the position that, if I understand correctly, Trump has lost a few weeks ago.
For that kind of use, owning Tweeter, with absolute control on content and a user base stoked up on anger against "the Libs", "the pedophiles", "the establishment", "the deep state", etc. would be invaluable.
There are a variety of problems with that approach — not least that he'd be aiming for the primary targets of oil company propaganda.