While I would not take our dog to the US (too many restrictions),
I'm curious: What type of restrictions do you mean?
I've flown with my dogs between the US and Europe a number of times. It's not something I like to do, but it was the best solution given logistics and time spent in the US when I've done it. (I can't say that they particularly loved it, but they weren't terribly traumatized over it either.)
It's been a few years, but back then the formalities of getting them in were no big deal. Verification of rabies protection (not by titer, simply by verification of the vaccine used, which vets here in Germany do automatically in the "Impfpass" it seems.) I may have had to have taken them to a vet a reasonable time before flying, with an appropriate note of their health in the "Impfpass" as well. Upon arrival, I had to pick them up from the bulky luggage (or similar) station -- they didn't send them down the normal luggage belt! There was an inspector who looked at the papers briefly and then looked at the dogs for a couple of seconds. That was it.
It was much more work to fly one of them into Germany from a non-EU, Eastern European country. Even though we had checked with the various government agencies in Germany and filled out (or had filled out) all of the appropriate inspections, verifications, etc., the kindly folks from Zoll at the airport weren't satisfied, My German was pretty rusty after years of neglect back then, and I couldn't figure out what they wanted (nor could/would they use any other words, even in German) to explain it. Eventually, they just gave up and waved us through.
The whole thing may likely have been complicated by the fact that the dog flew "unaccompanied" -- we had been back home for a few months and had just moved to Germany, so the friend who had been dog-sitting for us shipped the dog from the country in the East.