Matrix doesn't have any special way of avoiding that tradeoff. It just takes the other end of the trade: Matrix servers are exposed to valuable metadata, so that people can use whatever identifier they want.
And, of course, the flip side of Matrix's "freedom and liberty" federalized design is that it is May 7, 2020, and the project is just now announcing E2E by default for private conversations. This is exactly why, years ago, Moxie Marlinspike wrote his post arguing about the downsides of federalization. It sure looks like his predictions were borne out!
I think both of these projects are valid and important, and that they have different goals and audiences, and we do people a disservice when we pretend like they're in any kind of serious competition. Matrix is what you'd replace an IRC server with. Signal is what you'd tell an immigration lawyer to use for messaging.