Re: Bunker Hill, British general Sir Henry Clinton, “reflecting on the hazards of that day, wrote a trenchant summary of the battle: ‘A dear bought victory, another such would have ruined us.’ “
— Page Smith “A New Age Now Begins” Vol. 1 (1976), p. 531.
I think that you miss my point: yes, the Brits carried the field in that battle. But we and they realized that we were far stronger that anyone guessed and we weren’t going to crumble and fade away.
Bunker Hill/Breeds Hill was the first real demonstration that we were a power capable of fighting and winning.
The Brits won a hilltop at great cost but our forces preserved their combat power and moved on to our next battle. Strategic vs tactical victory.