No shelf under a range hood. Will do nothing but get extremely nasty and block the hood from working properly.

In a study by, I think, the California Air Resources Board, adding a shelf under a commercial hood (deeper and higher than residential hoods, and set at 7 ft above the floor), a shelf was found to have little effect on capture and containment. I don't recall the shelf dimensions. As the hood size and distance above the cooking surface shrinks to residential hood dimensions, I would expect more flow interference from a useful size shelf. Grease deposition would be, as noted above, a likely issue.

I have been debating this same issue. We installed a 60” hood and I‘ve gone back and forth on adding a shelf underneath. I was only planning on storing cooking utensils, as I know the heat would not work well for oils or seasonings, but after seeing my baffles, which get nasty (as they're supposed to when doing their job), I’m afraid anything up there would get really gross and hot while cooking. I will note we do a lot of high heat cooking, griddling, and frying, so we may be messier than most. I think I’m going to stick with a backsplash that is easy to wipe down. Not sure if that helps, but I understand your dilemma!