Spectrum is owned by the public, and regulated as spectrum is a limited resource. IP messaging isn't by any practical means a limited resource.
> As far as I know, as long as I have the right to use the frequencies, I could start my own cellular telco that transmits whatever format I want.
No. Spectrum is regulated in terms of what technology you can use, and kind of usage is supported. You can't buy LTE spectrum and broadcast radio on top of it, and vice versa. You can't (in most cases) take 2G spectrum and deploy LTE on top of it.
Interesting! I was not aware of that. Thanks!
For example:
If a carrier "owns" the block between 1900MHz and 1940MHz, and let's say LTE supports 2 bits/Hz using Frequency Division Duplexing (each direction, up and down, gets a chunk of spectrum), with 3 sectors per cellular tower, the carrier can support a total of 40x2x3 = 240Mbps per tower, or 120Mbps each way.
If the tower serves 1000 users (they serve far more in dense urban areas), each user will have 120kbps of capacity, and if they all use it at the same time, that's the speed they'll get. If there's a single user, the maximum down speed for that user would be 120/3 = 40Mbps.
Point I ("I have the right to use the frequencies") directly depends on point II ("whatever format I want"). When applying for using a certain frequency band, you have to specify usage and purpose, and you can't just change your mind, i.e. you can't apply for GSM frequencies and say you will be running a GSM network, but then run the PavelLishinOverAir protocol.
While this is mostly true, in practice (at least on the 450-470 MHz band I work with), you can give fairly vague purposes, like "telemetry" or "SCADA", and it doesn't matter what vendor or what protocol you use. In fact, there is no section of the licence that says "I am going to use protocol X on equipment Y manufactured by vendor Z" or any part thereof (emissions designators are a different story).
I don't have any experience will cellular licences, though. Given that carriers frequently repurpose spectrum as technology changes, I can't imagine their licences say "GSM only" or anything like that. The band that used to be 3G GSM is being used for 4G LTE on my phone right now.
The same regulatory body (BNetzA) is also responsible for licensing telecommunications providers in general. This is probably the crunchpoint - if you're not a licensed telecommunication provider, it's simply illegal to offer telecommunication services.