Cell towers could do all those things you suggest. They don't though. They just use a GPS receiver. They have an internal TXCO (Temperature Compensated Crystal

Cell towers could do all those things you suggest. They don't though. They just use a GPS receiver. They have an internal TXCO (Temperature Compensated Crystal Oscillator) or similar, but they drift eventually. 3G and earlier tech was actually more resilient. It could use GPS for more accurate timing, but didn't require it.