As someone who has installed a lot of roms, I recommend staying with the stock one. It can be really useful on very old phones, but it is not necessary on most current devices. The two biggest issues I had were the lack of floating windows and the play integrity api issue. Also MIUI (without bloatware) is the most useful Android interface. Pure Android is nice and simple but not suitable for everyday use.

🙃 There might be a few exceptions.

Is there a service that can’t be used without a phone number and has no alternative?

Avoid using services that ask for your phone number, for your own good.