With large live venues you are going to mic the drums anyway, so all of that "natural resonance" of the unmuffled or undampened drum is going to be lost anyway - it's not going to cut through because simply put, it's not loud enough.
I'm actually a fan of both muffling and leaving things be, but the context (IMO) should be considered. About the only place I'd want drums unmuffled would be for jazz in a small setting where the acoustic properties really do matter. Otherwise I see a bit of judicious muffling or dampening to be a good thing. I'm not saying to muffle things to the point of sucking all tone out of it, but a piece of gaffe tape or moongel can work wonders.
As for my bass drums I use a thin piece of foam on the bottom of the drum, lightly touching each head (soaks up some of the overtones) and I have small pillow that I adjust as needed - more pillow on the head if I need to cull some volume, less, if I want some more boom and less thud, but I don't have it set up to ring like I would have it if I was doing jazz.
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