i got winded walking up some of the paths on mount rainier, especially once we got up into the clouds. no idea what the elevation was.
and when i visit dad in colorado, there's a nice park w/ great hiking at about 8-9k feet and we do just fine there - even the kids did great, and my son was only 3 at the time. but you're right - there's something about 10k where the air suddenly gets a lot thinner. Monarch Mountain (a ski place not far from dad's house) says its base elevation is 10,790 feet, and Summit is at 11,952 feet. Ski Cooper (another one, not far from Leadville) says its base is 10,500, summit 11,700. i get a little winded just walking from the parking lot to the lifts. yes, it's uphill, and it doesn't help that it's hard to walk in ski boots, but still.
and i've lived basically at sea level my whole life. when i was a kid my brother and i would ride our bikes down to the seawall and go fishing. the part of houston i live in now is about 140 feet above sea level. so no real difference in air pressure between here and the beach.