These "pajama" bottoms are neither more nor less than thin sweatpants without the elastic at the ankle, covered with whimsical designs or plaids. All three of my children (college, high school, elementary school) wear them, often from the moment they get home from school. (They haven't yet been swept up in a fad of wearing them to school).
At my youngest daughter's birthday party this weekend, eight eleven year-old girls showed up in jeans or shorts, then immediately went upstairs and changed into the "pajama" pants they brought in their hands or backpacks.
My daughter's friends show up at the house after school and change into the "pajama" pants from their bookbags.
They may wear a pair to bed, but T Minus Four's probably correct when he says the girls don't roll out of bed in them and go to school.
Wearing pajama pants is no different from wearing sweat pants, warm-up suit pants, or (in my day) the pants from a pair of doctors' scrubs. They just happen to be called "pajama" pants. I would pick bigger battles to fight. If you want to prohibit sweat pants, warm-up suit pants, and MD scrubs pants at school, then I can see lumping these "pajama" pants in the same category.
Don't get caught up in the name -- these are just thin sweat pants covered with a whimsical design.
What I meant to add is that these are a current TYPE of casual pants called "pajama" pants. You don't buy a pair of pamajas and throw away the tops -- they are inexpensive (and obviously comfortable) thin sweat pants printed with whimsical designs.
I'll bet nine out of ten pair are worn for casual comfort and are never worn to bed as pajamas.