i think they will wear eventually if you repeatedly drop them onto concrete. that might also be the case for rubber mats, but it might prolong things. i'm not sure how much. i don't know about carpet.
in my gym we have concrete floors with rubber laid over the top. official policy is no dropping the bumpers off the platform because they reckon it damages the weights. nobody listens to that, though, and while some of the very very (very) old bumpers are looking pretty beat up they are still perfectly usable. they get a lot of use compared to a personal home gym.