My mom was able to get our entire extended family on Signal without my involvement, which is a testament to how easy that is.
Not whether that's a good idea is more debatable; you're not wrong about discoverability.
They stopped doing that (and I uninstalled Signal as a result), so they can also stop with the phone number thing, in fact, it would make more sense than with the current situation where Signal needs a phone number but doesn't use it (except for registration). I could even reinstall Signal if they do this.
If I want discoverability, let me provide my phone number.
If I want privacy, just assign a random identifier.
I'm not mad at all if somebody prefers using their phone number and not having a password for a service – just give me the option to use my email address and/or a username.
There are too many "phone number only" services out there these days.
Plenty of people are, and for good reasons.
In most countries, you can get an anonymous phone number anyway.
I know this will invite comments about usernames. I would like usernames a lot too.
The knowledge of how to do this has forever been lost. Hopefully archaeologists can reconstruct it one day.
It's also not a great idea to make sign-ups for an instant messaging service contingent on having an account with another, competing service.