Looking at https://matrix.org/faq/, I see this:

    Can I run my own identity server?
    See also: What is an identity server?
    Yes - the reference implementation is sydent and you can run your own ID server cluster that tracks 3rd party to Matrix ID mappings. This won't be very useful right now, though, and we don't recommend it.
    If you want your server to participate in the global replicated Matrix ID service then please get in touch with us. Meanwhile, we are looking at ways of decentralising the 'official' Matrix identity service so that identity servers are 100% decentralised and can openly federate with each other. N.B. that you can use Matrix without ever using the identity service - it exists only to map 3rd party IDs (e.g. email addresses) to matrix IDs to aid user discovery.

As someone that really likes Matrix because of its decentralized nature, I'm not really seeing a problem here. TBH, I don't really care about mapping a [email protected] to @foo:bar.com. All of my matrix contacts I've just asked them what their username is, then started chatting with them.