I'm a volunteer EMT in New Jersey and also a ham radio operator, and as far as I know, most places including our own use local radio systems like the one you describe. The license covers everybody in the agency (just like a taxi dispatcher's will). We use a two-tone system; the radio is squelched until the two tones come through and then the radio alerts (if it's set to alert) and unsquelches for the voice transmission. The earliest iteration of this was called a Plectron and the term is still used informally to refer to our Minitor portable pagers. All the neighboring agencies use variations on this system, but I believe the largest agencies (like NYFD) have some computerized dispatch. We don't directly get dispatched by neighboring towns for mutual aid - that comes through our own dispatch so they know to keep track of us - but if we are on a call to a neighboring town we are allowed to transmit on their frequency and have some radios that can do so.
We use VHF low band (~45MHz) for dispatch and used to use it for voice comms, but the antennas are just too long for portable use to be effective. Most nearby police are on UHF, and the regional emergency frequencies are on VHF. We have Motorola radios for each frequency band, each with anywhere from 4-20 channels programmed into them.
The decision for who gets radios that can transmit is mostly driven by cost and numbers. In our squad, all the crew chiefs have transmit-capable radios, and everyone else has a Minitor (2-5). The radios are 2-3x the cost of the pagers. We have about 16 radios that can be signed out for use by non-crew chiefs.
Every agency uses something a little different, and in most cases (especially smaller agencies) it's roughly the same system they came up with about 40 years ago. So there's a lot of historical legacy involved. The newfangled thing is trunking radio systems - those are nice because they provide talkgroups and make interoperability and provisioning straightforward - but you kind of need to move all at once since "normal" equipment won't work with them.