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Personally, I'm not a fan of the big lick or of walkers in general- yes they can be comfortable trail mounts but I leave it at that. Give me a sturdy pony any day.
I did ribbons for the Eastern Classic a couple years ago at Quentin. While soaring (using chains or chemicals) is illegal and cruel, there are humane way so creating that artificial reach. The walkers are bred to move like that- albeit with less "drama". A good rule of thumb to see if a horse as been 'enhanced' is to draw a line out straight from underneath his chest, typically in normal movement, their knees do not go past that line.

I'm not a huge saddleseat fan to begin with, but I understand it more now that I'm at a barn that actually rides it.

Oh, and the Big Lick is not new by any means unless you mean in the last two centuries relative to the entire history of mankind. The big lick has been around pretty much as long as the breed has if not before. Having flouncy horses was a big deal for plantation owners and such. The breed and class history is actually pretty interesting.

I think it looks pretty silly, and not at all horselike in my opinion.

While Arabs do have the front end motion (which can be quit dramatic with out artificial aids) only walkers have the "Big Lick"

Arabs have the own set of peculiarities (I ride at a big well known arab barn)

I don't see how ANYONE can find that attractive in any way. It does not look natural/ its not natural. I've seen a full TWH in a feild and she was not walking like that. I know the little head bob thing is natural. But those videos look like they're walking on their hindquarters and kicking their front legs. I don't see how anyone would do that on purpose with no training.