Turntable versus tonearm versus cartridge: which is MOST important?

Right. The comparisons have already been done. I’ve heard it myself, a couple times now. Moving the same Benz Ruby from a Graham arm to Origin Live Conqueror was a vastly bigger improvement than moving from the Glider to the Ruby. Have also moved the same arm/cartridge from one table to the next. Another huge difference.

What you need to keep in mind is any cartridge however good or expensive it may be, all it can do is wiggle back and forth and up and down. All that happens is the really good expensive ones let you hear more of the tiniest details as it wiggles around. But the cartridge itself, no matter how good, has no way of knowing what wiggles are signal coming from the groove and what wiggles are vibrations coming from the turntable and arm. It dutifully sends it all right along to the phono stage, the obscuring noise just as much as the music signal. 

Turntable and arm on the other hand, when they are the very best they produce vanishingly small detail-smearing vibrations. Because of this even a very inexpensive cartridge will play back so much more of what is in the groove you can hardly believe it. Whereas if you take a really expensive cartridge and mount it on a cheap arm so much of what you are hearing is noise from the arm and table you will wonder why you spent all that money in the first place. What a waste. It is even entirely possible you get to such a resolving cartridge and phono stage as to let you hear all the individual faults of the arm and table!

In other words your hunch is a bad one. The truth is closer to the opposite. Put your money into table and arm. Then cartridge.

I have heard and believe an excellent table/plinth is the building block for a good turntable.

Effectively the cartridge's job is to measure vibrations so the better the table and the tonearm the easier the job is for the cartridge to get the information.

Some people like car analogies - race tires and good seat and harness keep the driver in position enable a great driver to get more out of a car.  If the driver's not skilled then the impact of race tires and properly seating position don't really have an impact.

Many of us have had the experience where a medium or a budget priced cartridge sounds excellent on a very expensive turntable with a high-quality tonearm. I am among those who have had this experience. Therefore I would say the tonearm and turntable are most important. Which is really to say that you can’t get the most out of an expensive cartridge using a cheap tonearm and turntable. I guess I am more comfortable with that way of putting it.

I'm in the camp that the cartridge and the tonearm be at or near the same level. Tip either one too far and it's not a good match. On the other hand the table should be as good as you can afford.