Why has there never been a Tony category for best hair and makeup design? There have been so many worthy contenders over the years! The Hair and makeup complete the look of the characters in their costumes, why not honor them? I feel like this is an important category.
To go off of what Nateben2 was saying, I've thought for years that a great category would be for Best Special Effect. It could be a small number of nominees or something. But it could honor those magical stage moments - back in the day, it would've been the chandelier in Phantom, maybe the flying in Wicked, etc. Even though Spider-Man was a mess, the flying they did was still amazing.
In my 25 years in the business (mostly regional, a lot of pre-Broadway), it still is done with the supervision and final approval of the costume designer. There maybe specific shows in which the hair/make-up department is it own design, on equal footing, but it would be a specific show. For example, my next show, with eyes on Broadway, only has a director, choreographer, scenic designer, costume designer, lighting designer and sound designer in all our NY based pre-production meetings. I am sure we will add a vocal coach, dialect coach, fight director, and others later in the process, but those all report to another one of the creative team.
Most of the time, the costume designer is the one that talks to the wig or make-up designer, presents research, discusses his/her needs for the over all look of the show, and then is responsible, at the end of the day, for its execution.
So, I think we are both right - there are hair and make-up designers, but traditional breakdown of responsibility, in my experience, has them reporting to the costume designer.
That's why I use the chair example. Props will often have their own designer (and very often in regional theaters an entire department dedicated to making/pulling/buying props) - but it's under the uber-design of the scenic designer.
Projections, although almost always have their own designer / programmer, often fall under scenic or lighting - usually depending on which design it serves more. (Although we see with technology moving, if a show feels it will have projections, more then likely, this get's it's own department, and a designer that would have equal footing with the others)
That tends to the more "assumed" model, but if props, puppetry, projections, hair, make-up - or any other these specialty skills sets have a great import for a specific production - I could totally see a production giving those designs equal weight to others, and not making it a sub-set of another designer. And every show's hierarchy, and who reports to who, is always a bit different based on who's who in the game.
Mind you - often straight plays -- which I have done mostly - there is little to no guidance given to an actor about the specifics of their make-up, and they design it on their own, with perhaps just verbal notes given to them by the director, costume designer and, quite a bit of time the, the lighting designer.
But, I think to answer the original question - traditionally clothes, hair and make-up would have all fallen under one designer, the costume designer - and thus no specific TONY.
Now, if I think they should have their own TONY, that's another question all together.