Cats are not dogs
One of the reasons it's difficult to train a cat to stay off a table or counter is because, since you aren't there to keep him of 24 hours a day, the training isn't consistent.
Training a cat to leave your feet alone while you are in bed is not as difficult.
Of course since this is a kitten, time will most likely take care of the problem. But the kitten will not learn anything, if she is kept crated every night. What she might do is start to go crazy being cooped up and get into trouble during the day.
Shutting the bedroom door would be a better way, then she at least would have the run of the rest of the home. It still would not allow her access to her people though, which is one of the things that bothers me about the crating. If she is alone during the day when her people go to work and then kept shut up in a crate at night, she is alone way too much. She needs to be with her people. If someone is home with her all day, it is not that disturbing to me to think of the bedroom door being shut to keep her out at night. But again, she will never learn, if she isn't taught.
Cats don't get "angry" in the way you describe. Squirt training can be very effective if used properly and for the right things. A cat who doesn't like to be squirted will learn quickly that playing with the blanket mice will get her squirted and she will stop doing it.
Another option would be to keep the vacuum cleaner at the foot of the bed, turned on but not plugged in. When she goes after the feet plug the vacuum in to make it burst into life. Kitten will learn that playing with feet makes this scary machine go on.
Another option would be, when she starts the game at two a.m., that's when you shut her out of the room. Rather than just crating her at bed time. She will soon make the connection and find other ways to entertain herself in the middle of the night.
yes all these methods take work. It does take work and a little sacrifice to raise a kitten. Just locking a kitten up to keep her from doing something that bothers you will not teach her anything.