I completely agree. Hamptons are the reason I travel with my pillow from home. I like a semi-firm but springy pillow that stays cool. Not memory foam, but similar to the foam found in an egg-crate mattress cover. I purchase them from a specific seller on Amazon and it's the only place I've found a suitable pillow.
Every single Hampton I've encountered has saggy, synthetic down pillows that offer zero support and sleep incredibly warm. They're also square, which means if I roll from my side to my back, I fall off the pillow. Regardless of corporate or franchise or private ownership, HI pillows are almost always the same.
I have no issues with the pillows at DTs, Hiltons, HGI's, W=As, etc.