Apps offer built in biometric login, websites don’t. So that’s one difference, and maybe it’s also the answer to the question of why they don’t allow rooted devices which might allow bypassing biometric checks.
Tying account access to one small, portable, highly vulnerable device with questionable reliability is an inherently bad idea in my opinion. Lose access to the device for any reason (lost, stolen, dropped, the fingerprint reader fails or the phone simply dies) and you also lose access to your account.
I prefer to simply create decent login credentials and store them only in my head --- not in a app and not in a web browser either. This way, when (not if) my phone stops working, I can immediately switch to an older backup phone without missing a beat.
I tie my bank accounts to two devices in case one goes wrong, and neither of those leave the house to reduce the chance of getting lost or stolen.
Of course, the phone has Apple Pay and keychain access ...
The "benefit" of Apple Pay is that by regular use, I am constantly reminded where the phone is. The watch hasn't griped about leaving the phone home when I take a spin around the "estate" here, so I'll check on that today. Matter of fact, neither does the phone when I drive off, leaving the other Apple goodies home.
More settings to check.