Do session musicians enjoy the material they perform usually? I know they are all professionals and they know how to give a good performance, but getting into the material they are performing is another thing.
Another thing is I wonder what gets a young musician to think "I want to become a session musician when I grow up"?
From the (few) session musicians I've spoken with, it's pretty much what you'd expect: Some material they like, some they don't. There are definitely composers that the musicians respect more. But it's not different from any other musician. My best friend from college is a concert violist in a symphony orchestra, and he plays classics, pops, and backing to rock bands. He and his comrades like some more than others. Really no other way it could be.
As to why somebody would become a session musician, it's about the best paying gig for a classical musician (excepting the rare brand name musicians, like Itzhak Perlman or Isaac Stern or Yo-Yo Ma). Many LA session musicians are also in the LA Philharmonic and the Hollywood Bowl Orchestra, and it's a great way to supplement that income.