There are usually two different types of pillows in Hampton Inn rooms. Two of them are feather and two are synthetic. The feather ones flatten out, but the synthetic ones do not.
All Hampton Inns are franchised. Of course the hotel itself can't do anything about it. Hilton tells the franchised hotels what to provide, so the hotel can only do what Hilton tells them to according to their standards.
As proof by the fact that we all have very different personal preference, I think that all Hampton Inn pillows are too fluffy for my liking.