This is a great idea for a beer that has only base malts. However, if your efficiency is very high and you add water to compensate for that without adding more caramel or roasted malts if the recipe calls for them you get a (slightly?) watered down beer because you will have diluted the flavors. It will be much better to adjust the base malt before the mash, saving it for future batches as you also suggested.
The biggest problem with most kits is the grains are premixed and usually milled, so you can't just remove the base malt.
Brewing with higher efficiency will get you somewhat higher gravity (and alcohol), but generally not much more color and flavor from the steeping grains either, although finer milling might help with that, as does more thorough sparging.
That said, if given the choice, I tend to favor brewing at the bit higher gravity (and resulting higher alcohol) over having a bit higher volume with the risk of it tasting a bit bland.
Most recipes are pretty robust in variations of their ingredients anyway. Increments are typically in 4 or 8 oz, so it's not all that precise either. Then there are differences in the actual malts used.
So if efficiency of an all grain kit recipe goes up from it's designed 75% to an actual 85%, we're looking at a 13% net gain. That's significant! And as you said, that gain is not all across the board, from elements that may not increase much at all, to others that, due to much better conversion and/or lautering, are even higher.