This is why shutting down the right to strike is a short term approach: you can't make people choose to start or keep working in your sweatshop, so eventually you run out of staff.
What you can do, at state scale, is pass everybody through a services training filter and sit them under the sorting hat after three months to winnow out skills and potentials of interest.
Some are clear rejects, some are good for getting up early and walking perimeters, others would suit the motor pool. An occasional few will gel for traffic control, signal intell, etc.
The trick then, for a state, is to incentivize with carrots, sticks, patriotic abstractions like duty, etc. the ones they want for the jobs they have.
You can draft a doctor, from pool of doctors. You can't draft ATC, because there is no pool of spare ATCs. It would be like drafting air defense operators - there is no pool of them outside military.
I'm pretty sure some of the air traffic controllers for military airfields in WWII were draftees, just like many air defense operators were draftees before the military became an all-volunteer force in 1973.
If the recent news about moving lots of soldiers from EU Nato installations back home is true, they'll have a ton of trained active military ATC's available to use in the US soon.
If you're a government, you can; it's called a draft. The US seems to be preparing for it.