Hair algae sounds like the least of concern for me nowadays. I can't remember what's the last time I had seriously troublesome outbreak. In my latest build, I got a brief encounter with it. But it went away soon after decent size of CUC were added. Between CUC and tangs, there aren't much chance for it to establish. All the other nutrient perspective is irrelevant. I know that because there are still some hair algae in my tank, but they're all in the spot that hard for fish and snails to get to, like a narrow gap between two rocks. As soon as I move the rocks and expose them, they're gone within days. So it's not that they don't have enough nutrient to grow, it's that they're eaten faster than they can grow. Also bacteria might play a role there that slow down their growth, but that's a harder point to verify.