People are free to pay Beeper for a service and Apple isn't stopping that. Apple is stopping unauthorized access a private network they run.
In order to prevent competition, Apple does not provide services like Beeper an authorized way to pay for access to their messaging protocol.
To make a bad analogy, it is like Jack's Auto Repair selling a service that enables Honda owners to use BMW service centers. And then Accord owners expecting to go to their nearby BMW dealer and get warranty repairs to their Honda.
Apple has a simple solution here. Identify how many unique users are coming to the iMessasge service via Beeper's app and send Beeper a bill for one iPhone 15 Max Pro for each user.
If they weren’t concerned about competition, we would have seen iMessage on Android a decade ago.
If they wanted to provide iPhone users a default secure way of messaging competitor hardware, they would have pursued an open alternative to SMS before they faced antitrust investigations.
Right now a Verizon iPhone customer can't securely send a message to a Verizon Android customer without forcing their customer to download a third-party app and agree to its terms, and the carrier has no recourse to change that on their iOS devices they are selling to their customers.
Vaguely reminds me a little bit of the web browser antitrust days. Regulators will catch up soon. At least Apple is planning to adopt RCS finally, even though they missed their chance to be part of the formation of the standard.
Edit: Or Apple could release iMessage for Android and for web.
Especially if your thing is the "everything" thing.