Just getting back here. There were a number of things that made the hand-held possible and yes, not related to the network really except that, the cellular approach meant that you needed a microprocessor in the phone to handle the channel hopping and you of course needed cheap processors at the cell site to manage the radios and control channels. All of that was stuff that came after IMTS was developed. If you disassemble a brick phone, most of it is battery and heat sink.
The thing that made thin phones possible came later, that was digital technology which mean the radio could be switched on and off as packets got sent and received a technology called DRX, discontinuous reception, that came with 3G later on.
The exact frequencies used is sort of irrelevant TBH, that all just has to do with propagation and path loss which just changes the various engineering parameters like cell spacing and so forth.
The thing that got people hooked on cell phones was that you could carry it around. That was the game changer.
I have a slide deck where I do on cellular latencies, I show a picture of a brick phone and say, this was the wireless device with the lowest latency in history. Meaning, it was on all the time when connect. Something that changed with digital.
But being able to shut things down in between bursts of packets is what made the dainty phones possible :)