But I still need to keep the SIM card active or I could never switch phones (or reinstall the phone OS) without losing my Signal identity.

I cannot ever let go of the phone number I used to activate Signal. In practice, that means I need to keep paying for a phone tariff I may no longer want.

True. I was assuming most people have at least one phone number they want to keep long term (even if it's not always active with their cell). Note though that signal will also work fine with non-traditional services that provide free or much cheaper phone numbers like google voice (US), skype, or twilio.

It is true though that you do need to maintain a phone number. That is one of the trade-offs they made to allow it to actually be usable. I have not seen a better solution for encrypted communication yet.

How does the phone number tie-in make it usable? Phone numbers and SIM cards are about the most user hostile thing I can possibly think of.

What's wrong with the way Threema does it for instance, which is essentially to bind the identity to a key pair that you can back up?

Threema appears to optionally do the exact same thing. Signal eschews the flexibility to ensure more universal usability by being able to assume that anyone who uses signal can be associated with their phone number. An assumption that holds for the vast vast majority of potential users.

I don't see how making phone numbers mandatory makes Signal easier to use at all. There must be another reason for this restriction. Some say it's for spam protection.

Signal will work with Google Voice, but as far as I can tell you still need a smartphone to use it. Without that, you can't even set up an account because you need to scan an OCR code first.