Overly long nails are a health hazard, not trimming a cats nails when appropriate is neglect. An overgrown nail can get stuck and cause them to break a digit, it can make it difficult and painful to walk, it can also make the nail break off, which is painful and can become infected.
Most cats will grind their nails down themselves to some degree, not by simply walking but by scratching against something (e.g a tree, your couch), which serves the additional purpose of marking territory. A misconception you seem to have is that a trimmed cat's claws can't scratch, this is not the case, a cat is still able to hunt* or defend itself with trimmed nails. It will simply be less likely to accidentally hurt you (overgrown claws can still poke through while the claws are retracted for instance) and will have less desire to scratch at furniture.
Here is the humane societies take on it (my local and national versions of the society all have similar stuff, and my local chapter even provides free/subsidized nail trimmings).
Trimming a cat's claws every two to three weeks is an important part of maintaining your pet's health. Not only does a quick trim protect you, your pet and your family, it can also save your sofa, curtains and other furniture.
* outdoor cats hunting is a serious environmental concern and you shoudl take steps to make sure they don't catch anything, but that's a separate conversation.
P.S it is kinda a weird move to write as if SGA is not you.
That's my bad, I somehow missed the sentence where you said you were summarizing with AI, probably because I stopped to look at the OG thread right before that sentence.
They are, that's what scratching posts are for, you usually need both. when it's not enough you trim them. Like you say it's a continuous wear down, so they would never grow to a threshold where they need trimming if normal cat activities is enough to keep them short.
No, to use your analogy the axe is shorter, and might need resharpening (something a cat will do by themselves after if they so wish) but it's not really less effective. Not being able to stalk because the nails are overly long is a much bigger hindrance to hunting than blunt nails. Cats don't use their claws for the death blow, they use the claws for climbing and for holding onto their prey. They use their teeth to kill their prey. So long as the claws are sharp enough to pierce skin and maybe tree bark (which after trimming they typically are) then they are good enough to hunt. You actually don't want something that digs in too well, a cat would want to be able to let go of things by retracting their claws, something they can't do with overgrown nails. I have personally watched cats kill birds within an hour of getting a nail trim.
My hypothesis is that gyms are bad. Only young and old people need to go to the gym, other people should be getting that exercise by hunting antelopes like they did 12k years ago. the only thing stopping people from chasing after antelopes all day is that they are too tired from visiting the gym.