Wasn't it because of this complexity that the original GSM standard used a satellite up link from each tower and down link on every tower therefor not needing local telco's to handle the exchanges?
What? Not that I ever heard of.
Satellites links might be used, but are in general a last resort as they bring in a lot of problems...
GPS, though, can be and is often used a frequency reference.
The GSM network is not really complicated (at least wrt 3, 4 and 5G).
The towers do not call each other directly, there's a hierarchy of exchanges.
Some are controlling the radio base stations, that are mostly "dumb".
Some aggregate the traffic from many of these controllers and maybe also act as gateways towards other phone networks.
Some keep the administrative data and permission of each subscriber.
Some are dedicated to know where the mobiles are, and the mobiles make sure to tell the network periodically.
There may be a mix of functions, and in general, nowadays, there is a split from the controlling logic and signalling plane and the actual user data/voice plane.
When you send a text (or initiate a call, not much difference there) the whereabouts of the recipient are looked up.
In their supposed area paging happens: a broadcast message asking "Are you here?", in case the mobile answer "Yes, here I am" the call (or SMS data forwarding) can go on.
The SMS are stored for some time if the recipient is not available.
For a call, a circuit connection* is set up (for GSM and 3G networks) and the digitalized, compressed, voice is passed between the mobiles, that have in the meantime agreed on the compression format to use.
If you move from one cell to another, this circuit connection is seamlessly handed over to the new tower.
If you text/phone someone on another operator, your operator will just ask for a connection to their operator, that shall take care of the finding and delivering of the message/voice.
4G networks and onwards do no set up a circuit, and the packetized voice is treated as (high priority) data (VoLTE).
Most 4G networks, though, still fall back to 3G for voice calls.
How the links between all these nodes are physically realized is for the most part immaterial, as long as bandwidth, latencies and error rates are well defined and within the limits: copper cable, fibre, point to point radio or even satellites are only ways to move bits from one place to another.
The public Internet and the phone networks are logically separated, though they might share the same physical links, and of course many protocols (IP for one).
*Circuit connection: disregarding how it actually is implemented, it's "as if" a dedicated physical wire had been connected between the two end points.
All of the above is a bit oversimplified, but not too far from truth.