IRC has pretty much always been free without ads. You make it sound unworkable when it's become so much easier to run over time. And tons of forums are in the same category.
Also there isn't a way for people to pay their share of server cost for services like that. For your average non-video communication service your options are paying 0x or paying 50x.
IRC doesn't offer multi device, high availability log archives. IRC doesn't offer a lot things, actually. Fairly sure the standards don't offer persistent identity.
All the things you describe are achieved via 'bouncers' or dedicated clients living in a server that an impermanent consumption device like a mobile phone might be able to connect to.
No, they're not native to the protocol, nor are they required. However it's an open protocol. You are free to pick from a number of solutions that compose that goal.
I don't want to compose anything and neither does 99% of the world. It's a non solution and we're having the Dropbox announcement discussion 15 years later.
Then buy from a commercial service, just like many do for email. (Many more just use gmail in that context.)
Commercial IRC services? IRC Cloud comes to mind as one I've seen others use. Couldn't tell you how much it costs, how good it is, or if it leaks data.
Adding that doesn't take many resources though. It's because IRC is old and somewhat neglected, not because it would be burdensome to provide for free.
And some networks provide bouncers so they basically do have that. And maybe some IRCv3 networks, I haven't looked into that much lately.