Anyone Damp the insides of your Speaker Cabinets?

Probably would help a lot of inexpensive speakers sound better and not a hard or expensive tweak to try in most cases.

"The thinking is that most dampening simply smears and delays the resonate behavior without truly eliminating it."

I tend to think of it strictly as what it says, ie damping material in the textbook sense of the meaning of the word Damping.

Yes, it may sound worse or better than otherwise, or not much different at all. Par for the course for "tweaks". At least its an easy, inexpensive, fairly harmless and easily reversible one to try if one is so inclined.

I've done some DIY speaker maintenance projects on older speakers where I changed the volume and distribution of internal damping material as part of the repair and tuning process, but have never felt the need nor been sufficiently inclined to just muck with the damping of a new pair in good operating condition, especially if still under a warranty of any kind.

"Do most speakers sound best in cabinets that resonate as little as possible?"

I'd say the answer is yes.

Most but not all. Some speaker designs (Tonian comes to mind and a few others that I recall investigating) make cabinet resonances (as opposed to minimizing same) an integral and key part of the sound design along lines analogous to how a string instrument does the same.

My opinion is that designing a speaker and designing a string instrument are not analogous so I am not sure how well the analogy stands. I do not doubt however that speakers designed this way can sound very good indeed, at least in subjective terms at a minimum. its one way to get something more and/or different out of a similar box compared to others. Is it better or worse though? Dunno. I suppose it depends on the talent and ears of the designer more so than anything else.

I suppose one way to look at it is that resonances always occur and a designer can chose their approach on they are managed or controlled as needed to get the desired results. How much is right or best is something of a subjective determination, part of managing the science in order to deliver the art in a pleasing manner. But there is no single one piece of art that works best for everyone all the time. Like most things audio, in the end, it all depends. There is no single right answer. Like wine, ice cream, and all that. If you buy a nice bottle of wine and are not 100% happy with the flavor, there are many ways to tweak it to make it "better".