I wouldn't call you crazy because we did just that 4 years ago in mid to late July. Actually we didn't have reservations for our whole 3-4 week trip to NM, CO, and WY and really never experienced many problems.
We stayed at Gros Ventre campground in Grand Teton Nat'l Park without reservations. Of course there were not any hookups there and sites were fairly plentiful. But then we tried to get a spot up in Yellowstone....no deal. First, we had a 28' fifth wheel which limited the potential campsites and didn't help the situation. But when talking to the person making reservations she just said that July was very difficult without reservations in Yellowstone period.
Our alternative was to get a camping site up at Colter Bay campground near Jackson Lake in the Grand Teton Nat'l Park. The rustic campground was first-come so we got there early one morning and secured a site. From there we visited Yellowstone for a few days.
To be honest, we were probably better off staying in Grand Teton anyway. Our experience with the traffic and congestion in Yellowstone was a turnoff. I'd go back to Grand Teton for sure, but probably not Yellowstone. Maybe a camping experience in Yellowstone would have changed our minds, but I'm not too sure about that.
