Can commercial air traffic operate from uncontrolled airport, airspace?
I will answer your question with what we can see in Brazilian Airspace and its rules.

In Brazil, there are some airports - non towered, operated by radio stations - which give information such as wind direction/intensity and temperature and QNH. Based on this information, the pilot decides on which runway they will land or take off, and relays this message to the radio operator. The operator will only relay these pieces of information to pilots monitoring the radio frequency.

Those airports are not controlled, then, if there is any strike, flying visually, no control will be effective.

For example, ARU/SBAU is a non towered airport, and TAM Airlines operates the A320F there.