I agree with you there -- cold stabilization can make a difference in clearing a wine.but certainly did notice an improvement to clarity
Yup, you can add tartaric back.IF there does happen to be an acidity hit -- wouldn't an acid addition prior to bottling "fix" that?
Early in my career I made a lot of NY Finger Lakes French-American hybrids, which were all high in acid. I cold stabilized on my porch to reduce the acid, and it was generally effective. Clarification was a side bonus to the need to drop acid, but it never occurred to me to use cold stabilization simply for clarity.
Generally speaking, I'm cautious about messing much with acid. I've gotten into an add/remove yo-yo with acid a few times, and it never turned out well.
IME, kits from reputable vendors have good acid balance, so I don't mess with it. YMMV