The reason, of course is that polyester has a much greater fatigue life than nylon, perhaps 100-1000 times greater.
For nylon to last it needs to be oversized and thus less elastic, less manageable, and less economical. So for sping lines, polyester is clearly a better choice. What about bow and stern lines? When cruising I use polyester without complaint (I don't travel with my home lines, they are left in place), but it's not my boat that worries me for long-term mooring, it's the rotten pilings at my economy marina. Even so, nylon seems to give the required stretch.
Anchor rode? At one extreme we use chain; no stretch. At the other we use nylon; some much stretch it adds to sailing around and can actually increase side forces on an anchor. Some search for a happy medium by using a long nylon bridle or chain snubber. But for the latter to function properly it need to be quite long and quite thin. And chain has the advantages of easy handling on a windlass and great abrasion resistance.
I had an all nylon rode. Sometimes it was like being tied to a rubber band. I switched to all chain and kept using the stiff polyester bridle I had. In gusty conditions it felt like being anchored to, well, chain. So I changed from 5/8" polyester to a slightly longer 3/8" nylon bridle and found a happy medium. I don't like a super long bridle, because then the rope will lay on the bottom in shallow places and be subject to wear, since the apex of bridle moves a good bit. The thinner line won't last as long, but the anchor has a better chance of staying in.
Still, it seems the only advantages of nylon--or primarily nylon with a chain leader--anchor rode is economy and availability. I predict market forces--sailors choose either chain if they feel rich and conservative or nylon if they feel poor or weight conscious--have prevented the right polyester product from reaching common outlets. Alas, I've inherited and scrounged so much 3-strand nylon I will never run out.
Why such as esoteric subject? Research for a new article. But me think it will get too esoteric for general interest.