AIME is not "required" at MIT. There is a space on the application to list AMC and AIME scores, should you have them, but as people keep saying, that's just part of the larger picture of your passions and taking advantage of the opportunities presented to you in your context.
You should explore the Caltech board for more details on what they look for. From what I can tell, presenting a decent AIME score may be more important in admissions there. (Not that it isn't a plus for MIT! Just that for Caltech, there may be an expectation that many applicants will have such experience. Ben Golub, if you're reading this, feel free to correct any misconception I may have perpetrated!)