I'm dredging up various traditional arguments here, and as well as the free will one, there is the magic one, that if God kept intervening, that would disrupt nature, and produce a magical universe. This would be unintelligible for humans, and too inconsistent for animals, possibly. In other words, nature would become irregular.
A problem here is that this is indistinguishable from a universe with no God at all, as many atheists have commented. If there are no interventions, there is in effect, no God. This is how many people see it! If there are small interventions, as some Christians argue (somebody's ankle is healed, or God whispers in your ear), why not bigger ones, e.g. stop the holocaust?