I don´t think gating or specialised plugins are the only ways mixers deal with drum bleed. It all depends on what kind of bleed we are talking about. Ideally in a professional context you are aware of this already in the recording session, using microphones with a pickup pattern that suits the job and with netrual off axis response so that the bleed doesn´t interfere in a negative way.
If we only talk about drum mics bleeding into each other (not drums getting into instrument microphones, because that should be handled with acoustic screens or different recording rooms when tracking if you want the instruments to be separated) there is a distance rule of 3:1 to minimize harmful interference. You also place the proper mikes in a proper way, and ideally have a session drummer who can tune the kit and understands why the ride usually shouldn´t go 1" above the low tom from a miking perspective - and what kind of playing dynamics is suitable on a recording session, depending on what you want to do in the mix later.
In many cases the bleed is not unwanted at all, you often mix the kit by “filling in” the overheads and use room mikes for ambience and a fuller sound than you can get from close miking the kit. One important thing, that I think many mixers do as a first step, is to align the mikes by moving the different tracks in time where they match and switch polarity when needed (on snare bottom for example) so that no microphones are out of phase.
If you want to use gates or expanders it can be great if you want a particular sound, but they need to be set up properly and ideally triggered by a passband/sidechain so it only opens when the drummer hits that particular drum - but it depends a lot on the drummer, the kit, the miking and the room how successfull a gate/expander will be.
If you´re just triggering the kit, hi- and lowcutting the feed to “zoom” in on that particular drum is usually enough for triggering, or just using contacts (maybe paired with mics). I´d think most drummers/sound engineers working with triggers do that?
But, of course if you got to mix a badly recorded, badly tuned, improperly setup and not too well played drum kit there are lots of ways to try to solve the problem - one of them being spectral editing, but working in that kind of detail can take a lot of time (=money) and a specialised plugin can probably be an effective solution and get as good results in the end.