Edit to add: If your towers are as congested as they seem, the carriers should be aware, and the problem is likely a lack of available tower sites; either because of geographical considerations, site owners don't want towers, or local regulators don't want towers. Additional networks won't really help with that either.
TBH, this happens a lot in large stable industries.
The commercial mobile phone network was invented in the 80's. Comparing market behaviors during the industry's infancy to the behaviors of established industries is wrong. The market took some time to figure out best practices, for consumers and industry health.
20's years ago roaming fees and texting fees where expensive, but then corporations figured out unlimited packages were more profitable. We pay a set price now for texting for the month, but it still costs the carriers money for each text we send. The carriers just hope that the power texters balance with the infrequent texters allowing them to turn a profit. The same with calling.
I don't know if regional networks could compete with national networks. I just want to reinforce that market practices at the industry's infancy aren't the same as they are now.
What really needs to be done is the monopolistic elements of cell phone service like spectrum, tower, and backhaul provided at cost by a neutral (state owned) entity and the retail services built on top of reselling that.
The barrier to entry on a ground up cell network is almost impossible to surmount without billions in capital but an MVNO that can work on the same cost basis and network as the national chains?