I would personally hate this. For nearly every type race, I've been pulling double duty (hunting and hatching my type's eggs) and sometimes people are overly competitive. People have asked me to focus on hatching my type's eggs before - nothing malicious - and it's quite frankly, a pain. I've also seen people talking about how if they saw someone who wasn't on their team, they wouldn't click/clickback them.
Even if those things didn't happen, I'd like to keep my privacy. And for those reasons, I'm afraid I'm against this suggestion.