Turntable versus tonearm versus cartridge: which is MOST important?

Agreed, everything is important. Sound fidelity (like a chain) is only as good as it weakest component.

Nice try. Freebie rubber power cords are absolute crap. If I swap out my Moneoone Supernova for freebie rubber crap it is obvious. But it doesn't bring my whole system down to that level. It is worse, obviously worse, but still much better overall than "its weakest link."  

A system is the sum of its parts. The weakest link may be the smartest place to look for improvement. But it is not what determines system performance.    

The best table and tone arm has no chance against a marginal cartridge.

The opposite of what many of us have said. Based on experience. The best table and tone arm will make a marginal cartridge sound incredibly good. The best cartridge on a marginal table and arm will only let you hear very clearly all the faults that made them marginal in the first place.

Spend $150 on each the TT, tonearm and cartridge. Then put the remaining $9,500 into a cable! Shell out another $1k on fancy interconnect nail polish coating.

Case closed. Problem solved. 

Or rather than an unrealistic approach this of all or nothing mentality, why not use a more balanced approach and allocate your budget so that each component gets consideration?

Lastly, why is no one mentioning the phono preamp? This is as much a factor as the rest. Especially if you are using a cheap $50 phono pre built into an integrated. 

Dynamic_driven, because that is a different subject. Cartridges and phono stages to have to match within boundaries. Among a group of excellent phono stages it will most likely be the cartridges that make the largest difference. The job of the cartridge is much more difficult to perform well and the way it interacts with the tonearm is perhaps the most critical match in audio. You can jamb any phono stage into any system if you are so inclined. 

Here's an interesting article/take on this very topic - it's a review on the Rockport Sirius III turntable.

Page Title (iar-80.com)

Ok - I'll have the last word.  The turntable is the most important component ; ).