In general, solve problems in the same way that email does but add protocol support for realtime direct communications and end-to-end encryption.
Or you could have thousands of medium-sized companies that each operate nodes that interoperate with each other even though none of them is the size of Google or Meta, and users could choose one based on whether they want to see ads or pay a few bucks a year, or run their own if they're into that sort of thing.
> It just so happens that you need a certain amount of infrastructure to implement it, which is true of everything, even email.
The infrastructure you need for email is any functioning general purpose computer, including ones you can find in the trash, and a domain name, which you can also get for free if you really want to and in practice costs around $15/year to do it properly. Anyone with the inclination can do this and many solitary individuals actually do.
The infrastructure you would need for this thing would be even less, because the premise is that you already have an email address/provider, so all you'd really need is the ability to map a port so you can make a direct connection to the other endpoint -- or IPv6.
Whereas the infrastructure you need to participate in the PSTN... I think you're required to be a CLEC to even have a block of numbers assigned. If all you had to do was install Asterisk on the trash PC it would be something else entirely, but the telcos do a lot of regulatory gatekeeping, which is another reason the legacy phone network should be decommissioned and replaced by a modern IETF protocol.
Currently the only similar thing I'm aware of is https://delta.chat/en/, though I believe it does all of its networking over email, rather than only using it as a fallback.
I wonder what the pitfalls of using email this way are; it seems like a great way to get a free backend and growth-hack a chat app, so there must be some reason it's not more common.
It's the sort of thing you get when somebody builds it as a hobby project, or a skunkworks project escapes from a large corporation and is already open source by the time the MBAs get their hands on it. Or, in the old days, DARPA funding.
Point me to the existing IETF RFC for e.g. mapping email addresses as identifiers for use in a standard communications protocol for voice and video calls.
Not any more, at least for any semi-popular chat. The throwaway and no-names? Yeah you can, well until IF they get big. And well, they won't.