Buying generic cards would break the chain of trust as there's no guarantee that the card you're buying hasn't been tampered with, such as the private keys of the card already being compromised at the factory.
It is a good idea assuming you can guarantee the security of the card. Banks typically don't have an incentive to defraud each other by supplying backdoored cards, so banks could indeed partner with each other allowing people to go into any local bank branch, acquire a card and then call their bank to associate it with their account. Of course, you still have the identity verification problem there, as you wouldn't want an attacker to be able to associate a card they acquired with your account and then spending your money.
However, if you're going to solve the identity verification problem for the above, why bother with a card at all? We all have phones or similar computing devices that can act as a card (for Apple Pay & Google Pay, the phone literally simulates a contactless card).
It is a good idea assuming you can guarantee the security of the card. Banks typically don't have an incentive to defraud each other by supplying backdoored cards, so banks could indeed partner with each other allowing people to go into any local bank branch, acquire a card and then call their bank to associate it with their account. Of course, you still have the identity verification problem there, as you wouldn't want an attacker to be able to associate a card they acquired with your account and then spending your money.
However, if you're going to solve the identity verification problem for the above, why bother with a card at all? We all have phones or similar computing devices that can act as a card (for Apple Pay & Google Pay, the phone literally simulates a contactless card).