More specifically, Apple does not allow other apps to access the SMS capabilities of the device.
Technically, if you have a tap in for SMS sending say, via a server relay, you can absolutely use other apps to send SMS messages.
I think Apple has good reasons for not allowing 3rd party apps to directly use the SMS functionality, namely prevents issues with 3rd party apps maliciously using the functionality to send spam messages, for example
Technically a 3rd party app iOS app could control Messages running on a remote Mac. But it would be misleading to say 3rd party iOS apps are allowed to send iMessage messages.
Apple should ban SMS relay apps and 3rd party email apps by your logic.
