Yep. You can even run your own play integrity-like backend.

>This is something that could be addressed at least in the EU by mandating banks to allow alternative services or not use this service at all.

The EU mandates banks to be interoperable, and to guarantee the security of users. You can solve that issue by going through an alternative app that doesn't use play integrity and is PSD2 compliant so other banks let you call their APIs. It usually requires you to be a bank, and as a bank, you're really risk averse. So you use play integrity.