I've only played DQ5 and that was a feature then too. If you defeated monsters sometimes they'd offer to join your party. 5 even had the MC as a kid befriend a young monster as part of the storyline that grows up as the player grows up. I remember really liking this but I regrettably haven't played any other DQs.
I'm definitely dropping money on the definitive edition of DQ11 coming up, it looks pretty stellar.