The Matrix protocol is more or less an open, replicated database. E-mail is similar in some ways, but:
1: it doesn't define enough metadata ("this is an image", etc)
2: it doesn't handle backtracking well, if one of the recipient servers misses a message (servers are just supposed to retry a given number of times).
3: it has no security/authentication concept.
All of these could be bolted on regular e-mail, but calling it e-mail at that point would be a travesty, and we might as well call that a new protocol. And if we are writing a new protocol, we might as well take a few liberties to address the shortcommings of the first (one could argue against the last part).
That is all.
As long as data is stored in Twitter managed database, it would never work.