Turntable versus tonearm versus cartridge: which is MOST important?

In the end, the firing squad would be a kindness.

A mercy killing. https://youtu.be/H59iOnYAsY0?t=24

We can make evaluations based on relative $ costs, but again the OP didn’t make it clear whether $ costs differences should be considered.  The OP still hasn’t clarified what his point is, what is he trying to achieve, or is just curiosity question without any benefit.

above all is synergy. tt and whole system. 

sometimes 'super and expensive " does not equal to better. but that's just me. 

expensive stuff need more care and level of quality of whole system. for instance. there is much more than just the cart, tonearm and tt

The Cartridge>Tonearm>TT or however the configuration of the items is assembled are in my mind not able to one item set aside as having the most importance. In terms of replaying a Vinyl LP it is this trinity configuration that proves to be the most successful method.
Each item is this trinity are totally dependent on each other and each item success within this trinity is dependent on critical tolerances for the designs of mechanics and critical dimensions for the geometric interface between the items in this trinity.
All parts will need to interface within the very well known geometric parameters and each part will need to function to the accurate designed mechanical operation.
If a item can not interface within the trinity that caters for the meeting the critical mechanical function and geometric interface, then in my mind it is only then that the item will fall from being of importance within the assembly.
There are Various Brands, Various Purchase Values and Numerous Ancillaries on offer of Items to produce the trinity.
If the designs from these producers are capable to achieve the above then the ideal set up can be achieved at a variety of budgets.          

Normally one would expect the cartridge to be the most important.  After all it is a transducer - the others being microphones and loudspeakers.

However it is the turntable that is the most important.  First, there are speed issues.  This is expensive to get right.  The cost effective way is to get a Direct Drive.  Second is vibrations.  This is critical because the signal from a cartridge is magnified some 10,000 times form cartridge to loudspeaker.  So the smallest imperfections are audible.  Vibrations come from ambient vibrations in the room (typically from outside the room), footfall, the cartridge itself colliding with the vinyl wall (and often magnified by the platter), the sound from the speakers themselves hitting the turntable, the bearing.  All these issues can be resolved but not easily.  

Compare this to a tonearm.  They have their issues but the difference between an average tonearm and a top one is not as much as any other Analogue component, even including phono stages.  I bought a very high end tonearm from Origin Live, but with a few months I sold it and went back to my Jelco.

My ranking from most to least:
Turntable;
Cartridge;
Phono Stage;
Tonearm.