Leg muscles are a lot larger. You can easily stay warm while cycling or walking at a brisk pace in the winter. Less so when standing still and doing pushups or situps.
They probably picked cycling because it's easier to measure and there's less variation. And there's much more literature on it (e.g. Tabata/HIIT protocols). I feel squats properly done would be even better as more muscles are involved. With the added benefit of not needing equipment.
Or burpees.
Sure why not? Mix it up.
Probably. But I think the body gets Abit tricked when the legs come into play in a locomotive fashion.