My personal experiments match Audiofeil's. I've played cartridges from $150 to $12,000 on my $11,000 rig, and carts from $75 to $2,000 on various $300-1000 rigs.
At least one cheap cart (ADC XLM MkII) sounds miles better on the top rig than on any lesser rig. It has its limits, but it shouts no weaknesses. This would make a killer combo for a dance party. Really fun to listen to, though perhaps not critically.
OTOH, the $1,500-2,000 carts (Shelter 901, ZYX Airy 2) on one cheap rig were just awful. Every weakness and noise from the lower quality table and arm were spotlighted. I couldn't take them off fast enough. Carts as revealing as these (or more so) need a good quality table and arm.
This isn't to deny experiences like Mosin's. If a cheap cartridge is flawed, you might get enjoyable performance on (some) cheap rigs that happen to mask those flaws. Better performing rigs won't do that and the cartridge will sound like the trash it is. ;-) Even the fairly costly Shelter 901 can sound trashy in a really good system. It leaks so much energy into a tonearm that it needs a really damp sounding arm, which carries its own sonic penalties. As usual, it comes down to effective component matching.
Are $1K+ carts worth it. That's a personal decision, there's no universal answer. Can you afford it? Do you have the system to take advantage of what it can do? Do your ears and musical preferences actually care about what it can do? Are you prepared to do the constant extra work that high level performance requires (there's no plug-n-play at higher levels of vinyl playback). The answers will differ for each of us.
For me there's no question: I'd buy my reference cartridge again in a heartbeat (in fact, I've done so twice - I'm on #3). Since it's now discontinued I'll probably even buy a backup before they're gone. But I wouldn't bother if my table, arm and entire system couldn't provide the solid platform, steady speed, low noise- and sound-floor and uncolored, unrestricted dynamics that a top level cartridge needs to play its best.
For you, it's up to you.