Apple creating an API wouldn't accomplish much, since Apple still wouldn't have access to the SMS message streams. The mobile carriers would have to route SMS traffic to Apple's gateway, and they're not likely to agree to that, since SMS is a huge cash cow for them.
One possibility would be to cut SMS out entirely, by convincing the senders of these messages (banks, etc.) to connect directly to Apple's API instead of sending SMS. But the problem is that Apple's service is proprietary, and all the people on Android phones will be on competing services with different APIs. So banks would have to figure out how to talk to all these different APIs. This isn't a compelling issue for banks to be spending their efforts on, since any customer who wants to receive their banking alerts without using SMS already can: these alerts are also available via e-mail, which is an open, universal and standardized protocol.
An alternate approach would be for Apple to create an e-mail to iMessage gateway that would give each user a dedicated e-mail address that would forward to their iMessage stream (similar to the many e-mail to SMS gateways that currently exist). Users could then subscribe that e-mail address to their banking alerts. Another advantage of avoiding SMS entirely is that it's an unreliable protocol, in which 1-5% of messages are lost. So if your alert is actually important, you may not want to entrust it to SMS in the first place.