Not particularly seen this view put out there, but in my opinion it would be pretty logical from Elon Musks point of view to use Doge as a form of twitter native currency.
Why? Twitter could just act as a type of custodial solution, facilitating a huge number of transfers of token amounts between users at no cost. He would have little interest in it being any more useful for users except in that internal ecosystem - see his attitude towards substack links etc.
Secondly, it continues his lukewarm attitude towards Bitcoin, for whatever reason he holds it.