A large number of services that send various billing etc things via snail mail and email also send text messages. The other part of this is that almost everything is automated these days for most people. Bill payment etc happens automagically. Most necessary notifications occur via phone apps.

Ignoring email works just fine, as evidenced by the fact that the majority of people I know don't check email unless it is for their work. Zero impact on their lives. It is the same with snail mail. I think I check my snail mail 6-8 times per year mostly so that the letter box doesn't physically overflow with junk.