The OP asked about relative IMPORTANCE, and most guys responded with a COST analysis. That's just one reason why the question is so complex. On a cost basis, I have often found that a very fine turntable and exceptional tonearm can bring out unexpected qualities of a relatively inexpensive cartridge, but that's where the complexity of the question enters into it. If the inexpensive cartridge can sound so good, it is also an indication of how poor is the correlation between cost and performance, for phono cartridges. If you leave out cost, all 3 components have to work well together, else you will never get the most out of the cartridge. So, I don't know how anyone can say that the cartridge is vastly more important than the tonearm and turntable. (The OP says "80%" for the cartridge. Some others estimate an even higher percentage contribution from the cartridge.) Cartridges fall right on their faces without the contributions from turntable and tonearm.
Breakdown of Turntable Performance
Over the years I've read numerous reviews of turntables, arms, platters, and plinths. I always wondered how much these individual components contributed to the overall sound. Here's my take:
Cartridge - 80%
Arm - 10%
Platter - 5%
Plinth - 5%
Cartridge - 80%
Arm - 10%
Platter - 5%
Plinth - 5%