I've recently upgraded the connectors on my Toxic SW22 (silver/gold) cable for my HEKse. With the conclusion that the connectors are also very important and well worth getting the best available for that cable. I fitted the connectors myself and, despite my dodgy amateurish soldering skills (using Oyaide silver solder), the SQ differences were obvious from the first few seconds of listening.
My SW22 originally came with own-brand Toxic gold-plated connectors as these were the cheapest. They looked good with a carbon fibre-like finish, but made no claims to any audiophile credentials. When I upgraded from HEK V2 to SE with larger sockets, I replaced the 2.5mm Toxic jacks with 3.5mm ViaBlue gold-plated - a bit more expensive and very well constructed, but still no claims to any audiophile credentials. This was a couple of years ago and I can't remember if I noticed a difference in SQ, which suggests that the difference was not memorable.
More recently, I swapped the connectors for the best I could find. The key audiophile credentials for both AECO and Furutech is that the pins are one piece end to end milled from solid metal; and the core metal is copper rather than nickle/brass/etc. Whether these two factors matter in practice can only be determined by listening.
First I replaced the ViaBlues with AECO Gold plated. I could have chosen rhodium or silver, but went for the allegedly warmer sound of gold plating to see if that tamed the HEKse's slightly forward nature. The AECO's did inded have a slightly warm presentation, but the fundamental benefits were across the board - all the usual cliches. On a practical note, these tiny plugs were a pain for an amateur to solder and I wasn't impressed with the cable strain relief mechanism, but for SQ they were worth the £80 per pair.
Then I replaced the Toxic 6.3mm jack with a Furutech rhodium plated. The SQ improvements were also across the board, but it did follow rhodium's reputation by imparting a more neutral and transparent overall presentation that rather nicely balanced out the AECO's warmer gold presentation. Because there's only one plug to change, it's even better value at £40.
Whilst I could immediately notice the SQ differences, both connectors then suffered from a burn-in period. I've convinced myself that this is not just me getting used to a new presentation - because the sound could flip one day to the next, from say a bright forward presentation to dark subdued and then back again. I felt the gold AECO settled down after about 1 week, and I'm still not sure if the rhodium Furutech has fully settled after 2 weeks. Of course, the longer the period the harder it is to determine what's what, but I've satisfied myself that some of this is due to real burn-in. So when people think they're hearing new headphones burn-in, it may be the headphones themselves, or the cable, or the connectors - I suspect it's a combination of all three.