On a long climb the breathing does not get easier. Anyone who tells you otherwise is describing a different hill. What changes is that you stop reading the hard breathing as a sign something has gone wrong and start hearing it as the sound of the climb.
Breathing through something is not a solution and has never pretended to be one. Nothing about it shortens the gradient or flattens it.
What it does is keep you in the situation long enough for the situation to change, which is how a surprising number of things end: not solved, just outlasted by somebody who kept going in and out.