>I'd be curious to know the banks you're talking about

Fortuneo (internet-only subsidiary of Crédit Mutuel) and LCL. I have had both their apps installed at points in the past. In both cases they defaulted back to SMS 2FA upon uninstalling, though I remember worrying I would have the problem you describe.

Ultimately I can't see how a bank could get away with forcing (rather than just pushing) existing customers to install an app. This would surely be a breach of contract.