Yes that's the point, Beeper are probably hoping Apple sues them for the reasons you describe.
> criminal liability by violating the CFAA and committing computer trespass
This is pretty tenuous. They do have proper authorization because the keys in question are valid iMessage keys and they are being used by the same individuals those iMessage keys are allocated to. They're not trying to commit any further crime post-access.
> violating the the OS license agreement and ToS [...] (yes that supersedes DMCA exception)
Does it? This seems like a pretty textbook case of reverse engineering for interoperability.
> reselling Apple’s IP for $2/mo
Probably the case they're hoping for a lawsuit on - the degree to which Apple has legitimate claim to control use of the iMessage protocol given their market presence. In the process of the lawsuit, if Apple is found to be leveraging this protocol anti-competitively, they're in trouble.
And beyond that, Apple is a highly litigious company with great lawyers and extremely deep pockets and large incentives to defend their ownership of the messaging market.
That they've been this slow to sue Beeper probably signals enough on its own that there's probably no field day to be had.