If you're running a game and you ask players for a short background, since your time investment is centered around those players having a fun time enjoying a world of fantasy & adventure, they should do as you ask. GMs/DMs need to have fun, too, not just players, and part of your fun seems to be integrating PC backgrounds into your adventure.

Try telling them about Howitt's "six-questions-that-will-help-you-make-better-characters"