I thought the only way in the US to prove your address of residence is collecting your last few phone bills and bank statements. It was a huge LOL moment, when I first heard about that.

Yeah, it's really odd and circular. You can often present a lease agreement if you're renting an apartment or house. If you own, you can usually present a mortgage statement. If you own and don't have a mortgage (because you purchased with cash), you can use bank statement and/or phone statement. But what's funny is, how do you get the bank statement and/or phone statement? You usually have to show a lease agreement, mortgage statement, or some other proof you own the place you live. It's fairly difficult for someone coming from another country to get those things when they first arrive because all the documents they have are from another country and the entry-level employees that have to take them would have no idea what to do with them. My foreign friends and neighbors have stories about having to use a secured credit card (basically a debit card but the machines think it's a credit card) for 6-12 months before they could get a regular credit card. It's very confusing (and arbitrary and broken) if you're not on the easy path.

Similar problems in many countries, there is usually no problems for the majority who lives there so the pressure to fix it is low.

This is true in the UK - driving licenses have your address on them, but for some reason they're not usually accepted as proof of address. I assume this is because you only need to renew the license (i.e. get a new copy of the physical piece of plastic with an updated photo and expiry date) every ten years, so in theory your driving license could be evidence that you lived somewhere nine years ago but not evidence that you still live there today.

Providing a recent utility bill or bank statement is a much more common ask.

Its definitely not the only way but it is an option for some people who don't have other types of id.