I think a cross-party Mastodon instance or something like it could actually be a good idea. The hard part would be deciding who's allowed to create accounts and when (or whether) to deactivate an account after a person stops fitting whatever qualification got them an account in the first place.
Being an MP, sure, that's a given. What about people running to be MP? What about people setting up fake parties / independently standing in order to get a place on there? Consider Count Binface. Clearly he should have an account on such a platform, but how the heck would he qualify without letting someone less sane on under the same criteria?
And then there's the fact it would need to be run by incorruptible third parties.
And the fact that fascist-leaning politicians would need to be allowed on there so they can't cry foul, despite the fact they'll all only ever post on X anyway.
But then, only a handful of MPs would use it even if it was the only platform available, so it being a potentially good idea is probably all it'll ever be.