Why I don't do single leg stuff in the gym
A lot of S&C coaches do, but I don't, here's why
Why do we put sprint cyclists in the gym? There's a couple of reasons, some more or less valid than others.
My reason is to make them generally stronger.
What does that mean? It means muscle growth - bigger muscles (myofibilar, not so much sarcoplasmic, hypertrophy) are stronger. Cycling is a skill, pedaling is a skill, building big strength needs to take place outside the realm of riding, you just can't make a ride hard enough to trigger a response similar to a 1RM or 5RM squat, deadlift or power clean on the bike, ie: to make you seriously strong you need to get off the bike. To get real strength gains outside of novice effects, you need big overloads and that can only be done effectively in the gym under a barbell doing big compound lifts.
If we take that as given (and not everyone will, and that's ok), then we're interested in muscle growth, which means overload, which means maximal loading on the muscles we care about. You can't do maximal loads on single leg lifts. You can get some benefits from it, but not as much as you can from a double-leg lift. Bulgarians, single leg press etc just aren't as hard on the triple extension muscles as their two-legged bigger brothers are. If anyone gets close to half of their squat with a one legged squat, they're wussing out on their squats.
So why would you do single leg work? Good question. Some would say because pedaling is one legged, we should train one legged, maybe, but that's the skill part of the equation and we have a very specific, very effective way to display our strength in a relevant fashion, and that is .. to ride a bike. To build the skill of holding hips stable etc, do very short, big gear efforts - standing 1/4 laps etc on big gears - 4-8 pedal strokes at maximal effort. I don't buy into the whole one legged thing and my riders who train in my gym never do one legged stuff (or any "core" mumbo jumbo, because all the Big 5 are core exercises anyway, but they're useful core exercises, not circus tricks) are as strong in the core and as stable on a bike as anyone you'll ever see. There's a lot of circus tricks and just plain silly bullshit done in the name of strength training, most of which is just wasting a trainees time.
Personally, I want my guys to be brutally strong, and to be highly skilled at displaying that strength - so we squat, we deadlift, we power clean, we press and we deadlift, and we do very short, high intensity work on our bikes in big gears. The guys at the AIS, the VIS etc, they love their one legged stuff, and that's fine, maybe at elite level you need it? I don't know, my guys are developing juniors and masters, not elites on the whole, but I think, at least for the guys I work with, one legged stuff is a sub-optimal use of their time for questionable returns. I also don't like legpress, I think it's a risky exercise and the removal of the trunk muscles to control the hips in a leg press is, I think, sub optimal, if in doubt, use more body rather than less (compound, not isolation, exercises). Yes, benchpress is similar to legpress in this regard, but it's a compromise exercise and is included for reasons other than developing relevant strength for sprint cycling. Your mileage may vary. Your opinions may differ. That's good!