Well sure. Gerrard was ready to go to Chelsea a couple of times, I think. But he didn't, and that's what counted. If he'd ended up off to Madrid, no one would have held it against him. Going to Saudi, on the other hand...
Sterling just has never seemed very likeable, somehow. And it may well be unfair, we don't know him at all. But he chose his path when he joined City, and carried on down it when he chose Chelsea. Those clubs employ mercenaries, there's no love there.