> one of the banks I'm forced to use checks for how it was installed, and Android for some incomprehensible reason is happy to report that to any application that asks

That's because apps that aren't published just on the Play Store but also on other stores or for direct sideloads (for users running Huawei for example which doesn't have Play Store) need to be able to detect the installation method to do updates on their own if there is no backing store.

The use case makes some amount of sense, but I think once an API becomes predominantly used for fingerprinting and the real use case becomes a side effect you should just nuke the API.

It's the responsible thing to do. Apple has done it a few times.