They won't even consider adding fibers to the foam due to the added weight. It's all about the weight.
I don't think that it is a stupid question. It is one that I have been asking ever since I saw that they sprayed the insulation on. Weight would be one issue. The only other one that I can think of would be loss of internal volume. I don't see where that would be an issue though. The biggie would be the weight.
I don't see why they can't just build the tank a little bit bigger to have more fuel for the additional weight, and burn the engines a little bit longer. I'm not a rocket scientist (I've always wanted to say that where it was actually a relevant statement) but I don't see the problem here.
I know that the added weight and fuel adds up to a lot of money to boost it to orbit (at $10,000/lb last I heard), but it seems like it would be a heck of a lot cheaper than losing the occasional shuttle and all lives on board.