OP, here are 2 ropes, both more than 20 years old.
The top one still feels firm and forms an eye when folded. The bottom one feels flat inside, the surface is much fuzzier, and it folds much differently with no force.
From a fuzzy sheath standpoint I'd climb on both.
From a 'how much does it fold' standpoint I'd only climb on the top one.
From an age standpoint I won't climb on either one.
And for you objectors, my hand is off to the left pinching all 4 strands together to avoid cheating or favoring either rope.
One time I went climbing to eldo with a guy that refused to climb using my rope. After 30 mins of arguing and deciding that neither one of up wanted to do the hike again to go get the other rope, I got him to agree to climb something 3 grades easier with him on the other side of the rope and me leading on the bad side.
Just one small flat spot in the rope, totally fine by my stands. Still a fun day no one died or permanent mental trauma.
It takes one spot to break a chain. Generalizing from a single occurrence is at least strange.