I have not used a grate in a long time (bird owner for 15 years.) I've found that my birds don't use the bottom of the cage at all if I have a grate down but they do occasionally go down there to scavenge/play when there is a flat surface they can walk on. Like you, I noticed that my birds had a hard time walking on the grate -- it looked quite uncomfortable for them. If the cage is large enough, the bottom shouldn't be completely covered with droppings by the end of the day and my birds seem to know to avoid walking in the stuff. You said that you sometimes change the paper more than once a day, so you obviously are paying attention to your little one's environment.
I've also noticed that the grate catches most of the droppings (rather than the droppings falling through the grate, they tend to pile up on the grate itself.) I find the grate much harder to clean than to simply replace the paper. I use "Cage-Catchers" cage liner paper that is cut to fit the exact size of the cage. This makes it a lot easier to put a weeks worth of paper down at a time and remove the top paper (curling it up to capture all droppings and loose seeds and other debris) each night. At the end of the week, the papers are all gone and this serves as a reminder to thoroughly clean the cage bottom and sides plus all the perches and accessories