Honest question about cartridge vs. turntable performance.

Faulty logic Chakster. Cutting a record and playing one back are not the same. Cutting requires more torque and consequently is more difficult to control. The cutting head is powered and is easily able to overcome any magnetic fields near by. 
Playing a record back is a relatively low torque situation with much less strain on the drive system. Now you have a very sensitive magnetic device trying to make sense of squiggly grooves. Any magnetic field near by is going  interrupt the process. The torque of a direct drive motor is now superfluous. A quiet environment is far more critical. You have to isolate the platter, tonearm and cartridge from everything. IMHO this is far more difficult than cutting a lacquer.
Vibration and noise is everywhere. You think your turntable is isolated because your rack is on concrete? Guess again. Keeping the motor as far away from the cartridge as possible is a good start. Suspending the sub chassis (what the platter and tonearm sit on) is another important issue. A suspension tuned as low as possible will isolate the sub chassis from any noise transmitted above the resonant frequency of the suspension. Vibration transmitted through the air is another problem. Putting your turntable in another room works. When I see turntables on a rack between the speakers up near the front wall where the bass is exaggerated I die laughing. That is the absolute worse place to put a turntable. Using a dust cover that is isolated from the sub chassis is another way of putting the turntable in another room.
In short for playback properly designed belt drives are the way to go. They may not be simpler depending on the method used to control speed. Some of the motors are very high tech. Just as high tech as any direct drive.  I think the Grand Prix Monaco and the XactAudio Beat represent the apex of direct drive turntables. They are interesting designs and I can not say how well they function but if I'm going to spend that amount of money on a turntable without a thought I would go for the Dohmann Helix. Total no brainer. It pushes all the right buttons. 
Direct drive turntables are great for DJ's and that is about it, not to mention the tonearms they come with are pretty poor.    

Atmasphere, in some cases it might be because they work better:)

I have to totally agree with chakster on his last post. The "noise" from a good DD turntable is vanishing low. Speed accuracy is superb.
What belt drive TT manufactures actually design and build their own motors? They just use an off the shelf product and in many cases it's a cheap product. They rely on the belt to smooth things out. Some state that they "modify" the motors, what's that mean, maybe shorten the shaft? And don't get me started on power supply upgrades. Some of the highly touted belt drives won't hold proper speed with out one. Isn't that the most basic job of a TT, to hold the correct speed?
BillWojo

Linn, the turntable manufacture argued that in a record player's hierarchy the turntable was the most important component followed by the tone arm and lastly the cartridge.
I think if you talk with a Linn dealer today, that same philosophy still exists.
The idea really makes sense, because you can not add additional information to a source, you can only reduce the information your trying to retrieve.(Or you can add additional distortion)
My advise is to find a dealer that will let you listen to different tt using lp's that are yours.
I think the Mobile Fidelity UltraDeck tt, is a great all-in-one set up.

You have to visualize the turntable as a system in which all of its parts working together in unisone gives you musical satisfaction . In your question if getting a given cartridge onto a better turntable will make the cartridge sound better is yes . Yes because if the turntable is better it will be.more inmune to vibrations making the task of the cartridge easier to track low level information. Being a system it is more complex then what I have explained but being all parts equal a better turntable should make a given cartridge sound better.