Well, you guys have me quite confused.
I've been reefing now for just over eleven years. When I started, I never had books or a computer to rely on, just the lfs where I purchased everything, and after about six months, I came across Julien Sprungs video where he promoted the Berlin system.
When I got a computer about 5 or 6 years ago, I found out I was doing everything wrong and one of those things was using tap water.
I purchased a tap water purifier and for several years used this for my water purification. However, I found it very expensive so I started to recharge the units, but as I added more and more tanks, the recharging was a PITA. Especially when I used so much to get so little purified water. (new cartridges lasted for about 22 to 25 gallons, and recharged cartridges lasted for 25 to 30 gallons)
Being that I never saw any difference in the tanks after using DI for several years, I went back to using straight tap water to see what difference there would be. I did this for a year and then went back on DI again to see if it made a difference this time. This time I only used the DI for a year and because I still couldn't see any difference, I returned to using aged tap water and have continued to do so for the last year and a half or so. Still no difference.
Out of 10 systems, the only tank with hair algae is the butterfly tank that a caregiver dosed copper to when I was on holidays many years ago. It is gradually getting better but it has been a lot of years since.
I have to clean my glass with magnets every 3 days for the reef tanks, and every 5 to 7 days for the fish only tanks.
I do NOT have any clean up crew other than a serpent star in each of 3 tanks. (no snails no hermits etc.....)
I don't know the TDS readings; all I know is a TWP cartridge only gets roughly 25g before recharging or replacing so the TDS must be up there.
If I'm using water like this in 10 tanks and only the one has a problem with hair, then the source water must not be the cause.
As far as phosphates fueling the hair, I would doubt this to be a cause as all the food we feed to our tanks has phosphates in them naturally and, most companies add phosphates to the products to preserve color and other preservations as well. (same as with all our foods we eat) Because I feed my tanks VERY heavily, and I don't basically have this hair problem, the answer I figure still lies hidden somewhere else.