Above FL 600 it is class E. It's in the AIM 3-2-6.
The reason the FAA "reccomends" using oxygen above 10,000' MSL during the day is because it's a BIG difference for someone to go from, say sea level here in DAB up to 10,000'. When I used to live in Vail it would have been no biggie, but I remember how winded I would get for the first week or so after I would return from a trip home to Chicago.
The FAA again "reccomends" the use of oxygen above 5000' MSL at night because your eyes need oxygen to produce rhodopsin. That is a light absorbing pigment that is produced in your eyes, thus giving us "night vision". You know when you wake up and turn on the light and you almost see a fluid like cloud dissapating as your eyes get used to the light? That fluid is the light absorbing rhodopsin.