Especially given the importance of teamwork. Competitive people tend towards tedious one-upmanship. It's something you want to screen out in the hiring process.
I had to compete for my wife, who supports me and inspires me and etc. me, with few constraints (such as no others compete for our affections).
I hate games of all sorts (they have rules and the fun is to remember them and play by them?). But nonetheless I realize:
Competition is for organisms.
It sounds like what you treasure most about your job is that you're released from competing. Finding a relationship is about fit, and a good relationship is about the investment you make. I've never seen competing to work in any phase of a relationship.