So far, I'd agree pretty much with all the existing 4 answers, so in the hopes of providing something new...
Backing vocalists, the good ones, have a career as a backing vocalist.
They will be working long, long after most of the acts they were booked to record/tour with have got their 5th gold star at the "Would you like fries with that?" establishment of your choice.
Very very few acts have an extended career.
Very very few backing vocalists are recognisable to the general public. Some of them quite like it that way. They do their job, they tour the world, or get to work in the coolest studios with a lot of current 'famous names'.
They'll still be doing that next year... & the year after... & the year after.
Some of them will have started out as 'young hopefuls', trying to carve their own path in the industry, but never quite made it. Others will have decided that's what they'd rather do in the first place.
Some go on to other things in the industry - a friend of mine, after first working as a member of a band with a couple of minor hits, then did BVs when a famous 80's band played in China as part of their world tour. She subsequently became a radio DJ, raised a family & generally enjoyed the whole thing.
Another friend, whom I first met in the early 80's, is still doing it. Power to her :)
Another friend decided she'd had enough after 6 or 7 years & went back to a "normal" life. She prefers that in her 50s she's not on the road all the time, nor in the studio til 4am.
I, on the other hand [echoing what user2842 said] had a couple of years at it when I was young... til the phone stopped ringing - as they say, it's different for girls ;-)