How good does a TT have to be for a good cartridge

Since turntable systems all work through vibrations, you want only the right vibrations getting to the cartridge. If the deck and arm are adding vibrations, the cartridge will pick them up. A better cartridge will more easily pick up those vibrations, as they can't tell which vibrations are the right ones (from the record groove) and which are the wrong ones (from the deck and arm). With an inferior deck that adds vibrations, the result is degraded sound.

Following this logic, you'd want as good a deck and tonearm as possible, as garbage into the cartridge = garbage out of it. I'm not calling either of your decks garbage by any means, but I'm not sure it would be worth your while to go all out with a cartridge. It'll most likely be similar to a great set of speakers ruthlessly revealing all the flaws of an inferior source or amp.

I wouldn't spend much more than the cost of the deck and tonearm on the cartridge. I have a Pro-Ject 1Xpression with Speedbox II and acrylic platter, and run a Dynavector 10x5. While demoing the cartridge, I got to hear the shortcomings of the deck. It's a great match IMO, but the 10x5 is capable of better performance. One of these days when I have more disposable income, more vinyl, more time to listen to it, and my daughter is older than 14 months, I'll buy a better deck for the 10x5.

Don't bother. 10x5 is okay, nothing more. I have it on my Spacedeck/Spacearm and look forward to getting rid of it. When you are ready for a better table/arm you will want a better cartridge too. But it will sound better on better combo, sure.
I belong to table first school. Then tonearm and phono stage, then cartridge. Putting $3k cartridge on those tables/arms would be a very strange undertaking, to put it mildly.

The 10x5 is OK and nothing more? A lot of people would disagree with that statement. I've heard a lot of cartridges on my deck for about the same price - Linn, Grado, Ortofon, and Goldring to name a couple - and nothing came remotely close to my ears.

I like the 10x5 but it is clearly not as good as a 17d3 or Lyra Delos. Of course, those cartridges are at least twice as expensvie, but still not in the stratosphere. I believe that the $1000-1500 range of cartridges give the best bang for the buck, which includes the Ortofon Cadenza/Kontrapunkt and Benz Glider series. After that the law of diminishing returns really kicks in.
Imho

The best answer is "It's complicated." There just isn't an easy answer because the table/arm/cartridge is a combination and some combos have a synergism and some do not. The issue is made more maddening because the types of sonic changes from an upgraded table are different from the changes with an upgraded arm or cartridge. I don't doubt Cousinbilly's story above comparing the Linn arms and cartridges; it shows how important the tonearm is, and I agree with that completely. However, improving the table the arm is on can result in some qualitative changes in the sound that, once heard, are indispensable. When I replaced my VPI 19 III with an early Galibier some 8 years ago, I was stunned by some of the changes----a profound sense of quiet that I had never experienced before; a lack of mechanical artifice; and a remarkable sense of see-through transparency. These changes were in addition to the normal audiophile stuff like improved detail, frequency extension, imaging etc. My conclusion was that a table upgrade can result in some qualitative improvements that cannot be achieved with a new tonearm or cartridge. So all 3 are important, but if I were to rank them in my order of priority, I would say the table is #1, arm #2 and the cartridge a distant #3. In fact, right now I have a $400 cartridge (AT 33EV) on my Triplanar VII and Galibier Gavia, and it sounds very, very good. Not as good as my Benz LP, but it doesn't give up anything I consider essential to listening to records. Going backwards on the table, however, would not be an acceptable compromise.