One infrastructure company wouldn't work so well. You'd need at least two, preferably 3, with the ability for the resellers to quickly and easily switch.
Here in New Zealand we have three providers, but we have national number portability. This means I can switch networks with no fees (unless I have a contract with a termination clause) and no number downtime. It helps competition a lot.
If it was a single infrastructure company, all cell companies could use the same towers. This would remove the competition of when/where you have cellular access due to location.
Number portability is already possible here in the US, and so long as I am not on a contract I can switch without fees.
Here in New Zealand we have three providers, but we have national number portability. This means I can switch networks with no fees (unless I have a contract with a termination clause) and no number downtime. It helps competition a lot.