On the landing distance question, I don't think that the theory is that a flatter slope is a good thing in itself if you land at the same touch-down point. The idea is that by being low, you will land right at the start of the runway (on the piano keys, as the RAF used to say) instead of a third of the way down it. That will reduce your total landing distance.
On the seond question, I, too, have flown with pilots who do it. I think it's very hard to justify in logic (though some other contributor may be able to do it), but intuitively, it does 'feel' as though it works. On an underpowered aircraft at altitude, you do seem to hit the target speed quicker.