I agree a regulator is not necessary to have a nice shot string. I can have a shot string with no more than 20 fps variation from my Prod, for instance, and some Turkish air rifles do better than this. It happens because the valve is harder to open when the air inside is higher in pressure. So when my Prod is at 2700 psi, the valve isn't open as long as when it is at 1800. So it goes from a short higher pressure puff to a little longer lower pressure puff and the pellet goes about the same speed.
The regulator adds an additional degree of adjustability and I would expect a longer flat shot curve, and perhaps a bit more flat shot curve, but it's very possible to have a nice shooting airgun without a regulator.