Yes, it’s a critically important part of the chain, just as important as the turntable itself.
Cartridges are transducers, like microphones, headphones and speakers. You probably already know how much these contribute to the sound you hear. These tiny little transducers are doing incredible work, converting groove modulations into movement via the stylus and cantilever, and then into tiny electrical signals, via magnets and wire. These must then be amplified, and that’s another story.
This work requires a staggering level of precision and materials engineering to achieve the best results. That’s why my Ortofon MC-A90 for example is so bloody expensive! You get what you pay for with anything that relies on precision and expensive materials. The cost vs. performance correlation is fairly linear; the more you pay, the better the results, predictably.
Cartridges can cost anything from $10 to $10 000 and their sonic performance varies from unlistenable to sublime. Spend as much as you can on a good cartridge. It’s a big part of the sound of a turntable, and better cartridges will last anywhere from 1000 – 2000 hours, compared to just 200 – 500 hours for a cheapy.
A good cartridge will also preserve your vinyl by causing much less record wear. The larger contact area of a Shibata or line-contact diamond exerts much lower pressure on the vinyl, at the interface between the stylus and groove. This causes less heat and therefore less wear.