"The X-Men make you do a will at 14."
If you die without a will ("intestate"), then your estate automatically passes to your natural heirs. Each state has a statute defining who those heirs are, and in what order they're considered. This describes the New York statute. If the deceased leaves a spouse, then the spouse (and any children) take the whole estate. If there's no widow or widower left, then the children get everything. If there are no children either, then the deceased's parents get everything. If the parents are already dead, then any siblings split the estate. And so on.
Most people die without wills. It may not be the wisest financial decision, but the succession laws often give the property to the people they'd will it to anyway. And some people don't have much of an estate to will.
With the exception of Warren Worthington III, I'd never really pegged any of the teenage X-Men to be independantly wealthy, so I'm skeptical that they have their own estates to will. If their parents gave them their money, then it's natural for that money to revert to the parents, as it would without a will. If Professor Xavier is somehow compensating his teenage wards for risking their lives before reaching the age to drive, then the Xavier School shouldn't be worried about black helicopters as much as little ladies from DFCS and child welfare.
Maybe the teenage X-Men are just willing their knick-knacks and trophies from adventures to each other. A will devoted to sentimental items rather than wealth. That would explain the need for a will without an estate, but it still wouldn't be binding.
Because in New York, you must be 18 to create a will. A will from a 14-year old is legally void.