: Maybe a dumb question, but if I have an electric drill, is there a good
: reason why I can't put various bits in it other than drill bits?

Efficiency. The higher rpms that you get from a router or a dremel tool work well with the very tiny cutting surfaces on those tools. Each time a sharp area on the tool bit passes the work area it scrapes or cuts off a tiny amount of material. If the tool bit moves slower then it takes onger to remove the same abount of material. Or, to put it another way, it cuts slower. a 1/4 inch drill tpically runs at about 1500 to 1700 rpm. A router, rotozip or dremel tool typically runs at 20,000 to 30,000 rpm. That is up to 20 times faster than a drill.

Now some tool bits have a substantial leeway in what speeds they can be used, and others really work best in a certain speed range. For example, with ordinary drillbits you generally work at a slower speed (RPM speed) with larger diameter drillbits than with smaller diameter bits. That is because the actual cutting speed is measured in the distance the cutting edge on the outside of the toolbit moves in a second, and with a larger diameter bit, it goes a longer distance with each revolution, than with a smaller diameter drill bit.

: For example
: those little sanding or cutting accessories that go with Dremels or even
: router bits?

Sandpaper cuts at almost any speed, so abrasive tools like that can be chucked into a drill. Just work slower.

: I assume those other tools have different speeds or maybe
: even better speed control, which could be an issue, but since the drill
: bit holder is adjustable, I don't see why it couldn't hold them safely.

A couple things here. First, the drill uses a chuck which typicaly has three "jaws" that move in unison to clamp down on the toolbit. this works well for centering the toolbit and is adequate for the speeds involved. With a router or Dremel tool the bit must be centerred a bit more precisely to prevent it fro wobbling at the highspeed that it spins at. These tools use a non-adjustable device called a collet that clamps the bit in place. Collets give a very limited range for holding the tools, so you'll find that almost all routerbits are made with 1/4" diameter shafts, some heavy duty routers actually take 1/2 inch diameter shafts, while the smaller motors on the Dremel tools and rotozip tools are holding bits that are mounted on 1/8th inch diameter shafts. Just 2 or three 'standard' sizes.

: Patsy (ducking in case what I'm suggesting is totally stupid and dangerous
: just to avoid spending money on more tools)

Dangerous? Well maybe. Stupid? Only if it is dangerous

Remember that all the tools we use today were at one time or another derived from cutting tools that moved at much slower RPM. At the dawn of the industrial age waterwheels or steam engines turned a large shaft that ran the length of a factory, and each tool was connected to that shaft by leather belts, just like the fan belts on your car. The shaft turned at one speed and each tool that needed a different speed used a series of gears and belts to obtain it.

Actually, you may be able to find a flexible shaft that you can chuck into your
drill. before the popularity of Dremel tools these were rather popular. There were some which had a gearbox that stepped up the speed of the cutting bit. Thus you could clamp your drill down (so it wouldn't vibrate off the workbench) and use this for your fine grinding or drilling.

At other times various manufacturers offered add-on accessories for electric drills. You could chuck on a reciprocating gear device that held sabre saw blades, A gear reducer that let you use screwdriver bits, and of course grinding wheels and orbital sanding and buffing pads. In almost all cases I've seen, getting the right tool worked better than getting a gadget for my drill. that's probably why you don't see a lot of these things still on the market. But, I have to say that I was pretty happy with the 5 inch sanding disk. I used that for cleaning up some small areas when I refinished a hardwood floor, and for the cost it was probably the best tool for the job.

Now, let's get back to solving your unasked problem. I assume you feel the need for a router to make bead and cove edges on strips -- and all you have is an electric drill. Well, you don't need the router if you use bead and cove strips.
Get a handplane for about $15 and use square edge strips. It takes about the same time for construction.

Hope this helps

PGJ