There is a mentality where if a service becomes ubiquitous enough, it should be treated like a public utility. It’s not a particularly valid way of thinking, but common nonetheless.
You mean if a monopoly is created, it should be regulated like a utility. Sounds perfectly reasonable to me, not sure what's invalid about this way of thinking.
The market in question is chat apps for the iMessage network, like Trillium was (is?) for many networks, not just "messaging".
See Reddit clients vs charging for API debate
If apple wants to shut down beeper, there is a very very very easy way. Release iMessage for android. And suddenly beeper is dead overnight. All they have to do is build the product people want.
Beeper's problem isn't implementing the iMessage API but providing access to Apple's infrastructure without authorization.
The answer seems to be Apple wants to force families to purchase an iPhone for every family member, or download and agree to the terms of a third-party app in order to securely communicate.
The difference is that Apple's business model is built around preventing you from communicating with iMessage while Amazon is happy to let you copy things from anywhere into or out of your Amazon S3 bucket (for a price.)