There's always an exception to every rule and statement. Bunker hill was a loss for us. The Brits took a shelacking, Pyrric victory at best. It's been argued that none of the British commanders who fought there were ever effective again. Having said that, the colonial militia were thrown off the heights and the British regulars accomplished their mission. That's what war is all about, accomplishing the mission.
Did it work out in the long run? Nope. At the operational level the Brits couldn't sustain their presence in Boston, left and didn't come back. Was that due to the American loss at Breed's Hill? No.

