When I started using my UDS drum, I let the grease drip and burn. That is part of the design. With only a single butt or brisket or slab of ribs, you likely won't get a grease fire going like this, but I do notice the flavor. Move up to yard birds, however, and the amount of grease falling is more noticeably. Some probably look at is as similar to gas grills that have lava rocks or like my Weber, "flavor bars". For that to work, you have to keep them burnt off or among other things, you can get a roaring grease fire going down below.
For comparison, I went over and inspected the vertical charcoal smokers the guys at Spice Wine Works build. Some of the very best competition smokers around. In operation, they are almost identical to a UDS drum. They include a drip pan to catch the grease. But they can load those smokers up with multiple slide in racks that would drown out the normal dampened down charcoal fires they use.
But after seeing that, I put a baffle plate on top of my charcoal basket to disperse the heat and a drip pan on top of that to catch the drips. I like the outcome better. It still develops plenty of bark without the burnt exterior. In a UDS you don't need to add water. It's just to keep the grease out of the fire. If you really load it up, it also helps keep the bottom of the drum from turning into a mess of ash and grease.
