The height of the front of the bike isn’t really what matters, though it’s convenient as a measurement (at least, the amount the forks have been raised with respect to the yoke is).What’s happening is the steering head angle has become steeper. This reduces trail: the distance between point on the road the steering head axis points at and the tyre contact point.Reduced trail means a reduction in the castor effect so the resistance you feel at the bars when trying to turn is less..Anything that compresses the front forks has the same effect so yes, braking, hard cornering or hitting a bump reduces trail and quickens the steering. As a result, raising the forks needs to be done with some caution, what feels good for normal riding may be unpleasantly twitchy during emergency braking.
Consider an extreme example of a "Chopper" style bike, with very long front forks at a much shallower angle than a regular bike.It will have great straight line stability, but there's no way you can flick it through the twisties.Raising the stanchions (or dropping the yokes, same thing, just a different point of view) will make the steering "quicker" but less stable as Fazerider points out.You could, of course, also lower the back end by a similar amount which would effectively negate the effect, although you might end up having to cut down the stand too or needing to replace the rear sets because you'd be grounding the pegs sooner.
The only gain there would be if you were short in stature.