I'm sure they would, but that's not the issue. The issue is my wish not to live in a brain damaged state with no hope of recovery. You would force me to do so, and place this burden on my family.
(Besides, we don't know for sure if the Schindlers would want to bear the burden without the $700,000, now do we?)
Your family will be obliged to execute your will so far as they can be bound. Just remember that you cannot control events in advance. It is a bit like trying to control how they will spend any money you might give them. The best you can hope for is that your intentions will be taken into account.
As for money as a factor in the Schiavo case, remember that Michael Schiavo had never pulled his weight, that until the settelment he was no more than a dependent in the Schiavo household. I am sure he thought about that.