"How did the film photographers handle this? Did they keep shooting reel after reel until they ran out, or were they more judicious?"
Well, In my film days, I shot mostly sports, but did landscape, portraits, and fine art work as well. I committed my first images to film in the mid 70s. I shot my first sports work in the early 80s. I can tell you this much...
I bulk loaded 10-20 rolls of film per game (tri-x), and we developed them, did our contact sheets, and printed a few. In terms of the actual shooting, having to actual focus with your hand, and wind the film with your hand really limited you in terms of how many shots you were going to take. ALL of us sports shooters went through more film when motor drives started to take off. At first they were just motor winders and didn't work much faster than you could move the lever. But before long we were at 3-5fps, and our 36 exposure rolls weren't lasting very long any more. Autofocus came along and allowed us to track action, and stay on the shutter, and another paradigm shift ensued. Sports guys were running around with 3 bodies on them.
On average now, I go through about 500 frames for college volleyball, and 500-1000 for college soccer. I tend to burst rather than stay on the motor drive. Sometimes I'll even shot in single mode, because I normally find the initial frame of my burst is the shot I really want anyway.
When I shoot portraits I am typically in single mode since the strobes have to cycle anyway. I do motordrive a bit for existing light work to protect against blinking subjects.
There are many types of photography and they have different needs. I've shot on cble releases and on 9fps motor drives. The only constant is that we do what we must to get the image we want.