A problem with IRC is that any individual IRC network is closed. Freenode shows how an IRC network can go rogue, and there is not much the users can do.
Matrix is a bit tricky. It is mostly there, but I wonder how many matrix rooms will survive if matrix.org would go down.
So, i can only give the view from the matrix.org server, but right now there are 248244 rooms with more than 2 users in them on matrix.org.
Of those, 124680 include users not on matrix.org. In other words, 50.2% of 2+ people rooms which exist on matrix.org are replicated and decentralised across other servers. Conversely, I'd expect there are tonnes of other rooms on other servers which aren't visible on matrix.org at all.
It'd be even more revealing to weight the stats by room size, as the bigger the room, the more likely it is that it'll be replicated elsewhere.
If a room only has a matrix.org name, how do new users connect to it when matrix.org is down? Maybe it is bug, but creating local aliases doesn't seem to work in element web. (Well, creating the alias seems to work, using it doesn't)
Then, how many rooms have admins that are not on matrix.org
In matrix, the act of participating in a room means your server gets a copy of it (with as much history as you choose to pull in). Anyone can add an alias to it, including after the canonical alias has died, if necessary. The alias setting UI in element web should be ok.
I can't do anything with a local alias, neither on element web nor on element android. The UI shows it exists, but search doesn't return it, joining doesn't work.
With element android I can publish the original name to the local directory, but that fails on element web.
Matrix is a bit tricky. It is mostly there, but I wonder how many matrix rooms will survive if matrix.org would go down.