You need to allow everyone to do banking via this resource and they should also want to use it as a bank. Otherwise you'll run into a situation where that bank is associated with risky customers and is thus treated based on that reputation.
If USPS banking helps the unbanked by only 50 units of help instead of a maximum of 100, it’s still a 50 point improvement. If Morgan Stanley or JPMorgan can offer me a better banking deal than the post office could, that’s no reason to not have the post office offer banking.
I agree it should be open to everyone, but don’t agree that there can be a maximum of zero-point-zero difference in customer base vs other banks.