It would not create a new blockchain but instead piggyback on an already existing one. You can attach a message to every ethereum transaction you send. This idea is simply using existing infrastructure to create a decentralized way to communicate.
Effectively this means the choice for users are going to be to either sign up for free on centralized twitter and never pay a dime for any tweet they send or have to buy a very volatile shitcoin so that they can pay a lot of fee (up to $60) to send a single tweet! Not to mention that in order to view the tweets of other people they would have to download the entire ethereum blockchain and most importantly index it which would take up a lot more space then search for the tweets they want to see.
Nobody is going to chose the alternative!
That would introduce centralization.