It's a really nice way to gas-light folks into submission: "The team has noticed that your mood has been pretty poor the last few weeks; is there anything we can do to lift your spirits? We're worried that your mood is affecting your work." <---- utterly horrifying
Now, I can't say what's going on in your team, and probably at the moment, all is well and nobody is feeling victimized by this. But consider the fact that by binding up two (properly) separate concepts (reporting of blockers, etc. vs. poor emotional state, which is a PRIVATE matter), you will be ruling out a lot of potential employees in the future. Your team could decide to change the policy as they please, but if I came in for an interview and heard about this, I'd run as far as I could.
EDIT: I have worked with people who suffer from depression and mental illness. I cannot imagine how stressful a work environment like this would be for some of these folks. I've been working at startups for years, and I have a thick skin—I can "deal with" the high pressure and culturally necessitated amalgamation of one's personal and professional life (even if I hate it), but there are a lot of really skilled workers for whom this is incredibly destructive.