No way I would tolerate replacing tires after every 3 or 4 packs either. We run on a grey felt-like carpet (I've heard it called Ozite, but I'm not entirely sure this is correct) with a slicks-only rule. A set of tires is competitive for around 3 race meets in my experience, (2 rounds of qualies and 1 main per class, plus one or two packs of practice). After that there's some fall-off but it's gradual enough that tyres can still be used for practice or racing if you're feeling cheap.
It does mean all the hassles of saucing, but sounds like we come out ahead in the end.