It should be pointed out that the context of the Bridgemen and the original Velvet Knights (80s and 90s) was generally a field of much more serious and stifflly regimented corps. Other corps would always march out onto the field (as opposed to nowadays where most just walk out and set up). Corps would generally play a warm-up facing backfield for one minute (as opposed to nowadays, where this is often a "pre-show" with ambient music, acting, etc.). Body movement for the musicians was mostly marching, horn carriage, high mark time, etc. (as opposed to the current use of body movement, ballet steps, dancing, squatting, leaning, rocking, etc.). Uniforms used to be more military in style (we still have military elements, but unis are now much more like costumes).
So the difference between, say, Velvet Knights and the other corps was much more stark in contrast than VK would be with the corps of today. VK used to run wildly out onto the field, sometime play their warm up right at you. Their DM salute was loose and laid back. Their uniforms ranged from tuxes and tennies and ballcaps, to straw hats and Hawaiian shirts. Their music programming was sometimes choppy, other times they played full charts.
My point is that the VK and Bridgemen shows of old would probably blend in a lot more in the context of more recent shows. While corps of today may not be trying to be funny per se, they do incorporate certain elements that are VKish and Bridgemanesque.