Two problems. First, it's going to be hard to get any kind of rigidity without heavy clamping that may damage the printer head. Second, the mechanism isn't designed to drive that kind of load. So you're unlikely to get usable results, and you are likely to destroy the 3D printer while you're trying.
If you really want to do that kind of work, you'd be better off with something like a CNC-equipped Proxxon micromill. But that's several thousand dollars' worth of investment for a tool that's honestly not good for much beyond what you're already doing with it - those things are tiny, so unless you're making intricate model parts or something like that, you're going to have a hard time finding uses for it that don't run up against the physical limits of what it can handle.
And, after all, we're only talking here about removing a thou or two of material that can be oxidized away just fine. Not that machining isn't an absolute joy, but a chemical process makes a lot more sense here.
I use a lulzbot Taz and the toolheads are easy to swap out. I've seen a dremel tool holder for it on thingaverse, so that would take care of the weight and rigidity since it would be on its own mount instead of mounted to the actual extruder.
What do you mean by "drive that kind of load"? Are you talking about the weight, or pulling the dremel through the material to cut it (resistance)? If the latter, it seems that just going slow with the steppers and a high speed on the dremel would eliminate that?
Other people have converted their 3d printers to CNC machines. I'm not sure why this wouldn't be possible with a little effort. It seems cleaner/safer than dealing with chemicals?
That may be true, but 3d printer gantries are not built for the stresses of a dremel or cutting tool.
First, you'll get loads of wobble. Normally cnc machines use a 2 smoothrod with a leadscrew in the center for strong stability and smooth motion. Once you turn on a source that spins in X000 rpm, it will send motion through the whole system.
Secondly, once you start cutting anything stronger than foam, cutting will introduce shear forces on the gantry head itself. All 3d printers don't need to worry about XY rotational motion. That's usually a non-constrained degree of freedom.
Third, you need to mount the piece you're cutting or it'll move (duh!). But tabletop vises are HEAVY. Your bed probably can't support it. The only bed I know that could would be a 3 point Z leveling bed. Those're rare.
Feel free to try, and not take my word for it. But this has been attempted, and failed on many accounts.