Yes, it is very do-able, with the right home equipment. Training has advanced in the last ten or so years to stay away from weight machines, as they only isolate one muscle group at a time. Rarely do we function with straight plane motions that use one muscle at a time. Take Mike Boyle for example, a strength and conditioning coach who is famous for working with pro NFL and hockey players, and olympic athletes. In his facility, there is not one machine that you sit on and isolate one muscle group. It is all functional related: bands, theraballs, foam rolls, medicine balls, balance discs, hurdles, etc. Yes, he does have heavy free weights, but if you're talking figure skaters, you don't need them.
Yes we do need free weights, but nothing above fifteen pounds or so (men a bit more). In most exercises, like a lunge or one-legged squat, you progress by standing on various balance challenges, then add free weights or kettlebells. 1/2 foam rolls or balance discs or key to progressing exercises, because as figure skaters, we are using our muscles to check our balance all the time. Plyometrics are also key, as the height you can jump is a huge measure of strength.
You can complete an at-home program with the following equipment: a theraball, balance disc or foam roll, sport cord/resistance band, hand weights, medicine ball, sliding discs, hurdles or step. I have not touched a weight machine in over 10 years, and at 34 can do all double-double combos consistently. (I'd try to get my double axel back, but I don't keep like to be able to get out of bed in the morning..
).
To the Mao Asada question: an elite athlete needs to work with a strength and conditioning coach, to monitor exactly what she is doing. But she can use all of the equipment above to accomplish her goals.