I sense its probably more of a logistics/safety issue.
We all know you can't effectively run an electric smoker on a long drop cord, can you imagine trying to go to a fairground and set up 40 or maybe 100 electric smokers... the people down the line would be at a disadvantage from those closer to actual wired electric, not to mention the load on the cords, and the chance of disaster with cords, wet grass in the morning etc etc.
Limiting folks to small wattage use for rotisserie and fans is different from burners.
Could you imagine if an unscrupulous competitor intentionally pulled a cord of a competitor... or if one came undone by accident and wasn't noticed right away....
Propane, would you really want say 60 people who you don't know, don't know their experience, don't know their build, to have propane bottles, the chance of flame out, and open flames in a somewhat confined space? I'm sure the folks providing the insurance for the event would have something to say about that, and the time involved in having more thorough inspections of units to ensure safety...
I honestly think the 'quality smoke' or 'anyone can do it' is just a nice way of saying, we don't want the trouble, hassle, or cost.
Also, its a tradition, it just seems more 'authentic' if its done over coals/wood. Sponsorship probably has a factor as well, but I'm sure they could get Masterbuilt or some of the other Electric/Propane companies to sponsor them if they were allowed, so that can't be all of it.
In the end, its their competition they are allowing you to buy into and participate, so they get to set the rules as they see fit.