with 4G finally getting fast enough (along with the low latency promises of 5G), i think we're almost at the point where what you propose might make sense.
before this, wireless tech/infrastructure just wasn't good enough, and needed continuing investment to improve. now that we're over the hump, a GSE can begin buying up the 4G infrastructure and leaving operations/service to the carriers.
since there are 4 national and some regional carriers, you could even divvy the duplicative infrastructure up between state and federal GSEs, much like state and federal highways. then you'd have some semblance of competition that would keep the infrastructure from just crumbling away from political/bureaucratic neglect.
before this, wireless tech/infrastructure just wasn't good enough, and needed continuing investment to improve. now that we're over the hump, a GSE can begin buying up the 4G infrastructure and leaving operations/service to the carriers.
since there are 4 national and some regional carriers, you could even divvy the duplicative infrastructure up between state and federal GSEs, much like state and federal highways. then you'd have some semblance of competition that would keep the infrastructure from just crumbling away from political/bureaucratic neglect.