One last meta point. We live in the wealthiest country in the history of the world, and the highest air travel prices (some part is a function of longer distances I know). We should expect that we have ample coverage, if not over-coverage, at all times for one of our major metropolitan airports. Pay them.
ATC should never work alone at any of the "Core 30" airports. https://www.aspm.faa.gov/aspmhelp/index/Core_30.html
Often Approach will take over the "tower" and operate in crippled mode (no clearances to cross active runways, you must go down to the end kind of thing).
Some airports are uncontrolled at various times and would revert to that. Some airlines would require the pilot execute a missed approach and deviate to a towered airport, others may allow them to land.