Is there any evidence that walking/running up and down the stairs is bad for your knees? The "folk-logic" being that particularly when you go down the stairs, each time you land, there is more of an impact on your knees (than when you are say walking or running on a flat surface).
Any activity that is done too much too quickly can result in injury.
However, many activities - that are slowly built up over time - can be done for an entire lifespan without messing up your joints.
Why is that?
The body is an amazingly adaptive specimen, full of biological tissues that can be altered acutely and chronically from a given stress stimulus, provided they are then given time for recovery and remodeling.
For instance, high-rate impact forces are good for bone. They signal the bone to go remodel and make denser tissue. But if you too much too soon, you'll get a stress fracture instead. Studies have shown that long distance runners aren't more likely to have knee issues say in life than sedentary folk. The runners who do are ones that have sustained injuries and kept on running with full recovery.
Not necessarily. With stair descent, there is loading place on the cartilage areas in the menisci and also between the patella (knee cap) and femur (patellafemoral pain). But as mentioned above, these tissues are dynamic, and can be remodeled to handle those pounded forces just fine as long as you progress carefully.
An anecdotal example - I've hiked down mountain trails with more than 10,000 ft elevation loss (think 10 skyscraper descents) in a day, and my knees were fine. There is absolutely no way they would have been fine if I did that with no previous training, building up from a few hundred feet, 500 ft, 1000 ft, 2000 ft, etc... over the course of months and years (there are various time scales for adaptations to occur).
So you could do stair descents all day without worry, provided you have conditioned your musculoskeletal system for it!