What's the motivation? Is it to avoid needing to share phone numbers? Will phone numbers be private after this?

People have long complained that Signal violated their privacy by requiring them to hand out phone numbers. With someone's phone number you can discover everything about them, even location - it's possibly the most valuable ID.

For example, imagine you are a young female giving contact information to someone on a temporary basis; you might not want to hand out your phone number everywhere.

Especially when signal can't even make phone calls or text messages, there's no need for it to know my phone number

It can...

It can't. Signal calls are over the internet, not the PSTN. And Signal removed SMS support last year.

just use a landline from some phone booth, done. You only need it to create the account, never again after that.

According to rumour: Yes and no.

Some people really cared about not publishing their phone numbers, and Signal emphasises user compatibility. In a way, Signal aims for the best security that an IM can provide while being usable for a wide audience.

Telegram has this. It allows you to hand out your nick name and start conversing. If you want to get rid of that person you just block them and they don't have your phone number to call from a hidden or different number.

I have no idea either since:

"you’ll need to install and run a new build (links below), and register for a new account with a phone number (you can use the same one you’re using in Production)."