Won't this add everyone on the team as a code owner and therefore as a code reviewer on PRs?

Yes. I thought that wasn't the best idea either, but this is what has been done in our other repos.

Do you think that we should add individual owners to repositories?

Yea so it adds a lot of noise. Emails are already noisy and so I use https://github.com/pulls/review-requested to be able to really tell which reviews I need to take a serious look at. With this change, I'm getting included on all sorts of reviews and its not super clear which ones I really need to take a look at. Having individuals as code owners could work and when an individual picks up a driver they can send a change to this file to add their name. Similarly when they leave they can send a PR to remove their name from this list. Its slightly more work, but it would be distributed to the individual and this shouldn't get updated too often