Hopefully no one will call you stupid, but I've never seen that question here before! Y'know what they say... the only stupid question is the one not asked! (Not sure who the "they" are.)
Anyway... while I suppose you could technically do what you're saying, the problem I see is that there are a lot of thing in the NEW salt mix that is used up between water changes. If you took a cup of NEW dry salt mix and compared it with a cup of whatever was left after you boiled down some old used water, it would not be the same. There are "trace elements" in the salt that are supposedly, more or less, the same as what's found in natural seawater. Your coraline algae, corals, crabs, snails, and fish use some of those trace elements. In addition, there are buffers that help maintain your alkalinity and your pH that are depleted as time goes on. (You were on the right track... it would definitely affect your pH levels, if nothing else.) So yes... you would reclaim the "salt" aspect of the mix, but all the other stuff that your tank needs would be missing because it's been partially used up.
At least that's my armchair scientist reasoning for not doing it!