Most likely your other thermostat does not have a cool profile (check on the Analyze page). The time to cool uses this data to figure out how long it should take to cool the home. I often see this in multi-zone systems where one mode does not run frequently in a zone. For example, a first floor zone might almost never run cooling in the summer, so there’s not much high quality data, which results in no profile being able to generate, which results in no “Time to Cool”.
Not a whole lot you can really do to combat this unfortunately. I’ve toyed with the idea of trying to generate lower quality profiles but haven’t had the time to try it.
As far as “System Health” - that’s something that likely won’t ever come to beestat…at least not in the way you’re thinking. I dislike anything that interprets performance as “good/bad” because that’s very subjective. I think there are a few feature requests, though, that suggest displaying more data related to system health, which the user could then use decide whether or not things are running well. Metrics kind of do that today, but don’t really look at the same category of things.