There's redundancy in modern climbing ropes too. The part that does most of the support is the core. The sheath surrounds and protects the core, but is plenty strong on its own. If the sheath is cut through, the rope won't fail. Even if the core (which is composed of 10-30 strands each capable of supporting your weight) is partially cut through, the rope still won't fail. Of course, you are expected to inspect your rope regularly, and retire it if the core is exposed at all, or if there are signs of core damage.

The reason for retiring a rope when the core is exposed is not because it won't hold your weight, it's because there's no longer as much redundancy.

Climbing ropes (almost) never fail. There have been very, very, few accidents caused by this. You're more likely to get hit in the head by a falling rock while standing near a rock structure (something that non-climbers regularly do without thinking twice), than for the climbing rope to fail

I just looked at https://en.wikipedia.org/wiki/List_of_aircraft_structural_fa... and saw that there have been 2 recorded cases of airplane wing failure in the last 20 years.

There are probably more 'climbs' where a climber trusts the rope to hold their weight on descent in a single day than there are flights in a year, so I think the integrity of a regularly inspected climbing rope is the least of your concerns

(for some additional anecdata, in a 2 hour session at my climbing gym, I might participate in 10 climbs and witness 500)