Yes you want a phone for SMS to log on to the web site. But I avoid banking apps on a phone. Dont need them.

Choose a different bank, then. I've gradually stopped using the phone apps, not really by design but just because I don't often feel like that works better than the real web site. Both USAA and my local credit union have perfectly good desktop web sites.

I never do Banking on my phone and never had an issue.

I've never really experienced that. Which banks?