Nope. Public employee unions bring zero value and this incident is not evidence to support such unions. Relying on unions to act as ersatz safety regulators would be stupid, just completely the wrong approach. Decisions about things like ATC procedures, staffing levels, and training standards should be the responsibility of apolitical career bureaucrats.
Why would a career bureaucrat be a more efficient way to figure out how to attract and retain ATC workers, ass opposed to a union representing those ATC workers?
Your proposal intentionally injects inefficiency and noise into the system because you don't like some political boogeyman.