I've never bought a Dremel. But one thing I've never done, is cut out bad core. That might be worth it right there(I can't think of anything I have that would do that well).

But as for cutting door casings in place or nails and surgical removal of something, I usually reach for a hand tool. A nice pull saw and a block of wood is a joy to cut casings for flooring, and it's quiet and dust free and very fast. And fine metal blades in hand saws are good surgical tools and again with a lot less fuss for me(I'm on my third sawzall, that still gets used a lot).

My favorite tools are hand planes, chisels, and sharp hand saws so I'm not a good one to compare.