While it is (probably) true that we get more plays on weekends, -everyone- gets more plays on average, and everyone has the same chance to get a good card at the oracle for the weekend. Therefore, it seems fair to me because when averaged over time, nobody has an advantage in this regard.
The idea of losing something like 1 or 2 hp per play, rather than a cumulative loss per day, does seem interesting, and I think that would work. I also think the current hp loss system is fine, though, and doesn't really need to change. I don't like the idea of basing hp on the win/loss record; I think that it would result in less turnover in the top arena decks, and I like to see fresh ideas.