Carpet cleaning sounds like it's petty, but when it's SEVEN years of built-up dust, dirt, and God knows what else has been tracked in from outside (and remember, this is the Pacific NW, where there's rain, snow, road deicing chemical, pollen, etc), to the point where it's triggering asthma attacks in people, that's a serious safety violation. When the physical work space affects people's health and management's reaction is to roll their eyes and say "deal with it," that's some serious disregard for the health and safety of your employees right there.
It's probably actionable. No one should have to work in an environment that makes them physically ill, or exacerbates conditions they already have. An indoor office environment should be free from problems like that, it's not a freakin' construction site where you'd expect dust and dirt to be all around.