Poker involves a huge less amount of communication than our game. In poker, the game state can be held by throwing cards at the dealer, pushing chips into the pot, and doing a check tap. In pokemon, players need to be much pay a huge amount of attention to the game state. Having a distraction is never good. Moreover, poker is a very psychological game. Listening to music is a good strategy to avoid having any tells. I can know EXACTLY what is in your hand and still not know what to do in Pokemon. Clearing your mind is not a strategy unless it comes down to me Cyrus Initiative or Judging you (or obviously TGW).
There is a level of disrespect behind listening to music as well. Whether or not it is intentional disrespect is unimportant. It is still disrespectful. It really bothers me when my 8 year old cousin finishes his meal at a restaurant and pulls out his DS. Even worse is when he pulls out his DS BEFORE the food even comes. The disrespect is far from intentional (he's 8 years old), but it is clearly there. People listening to music while playing a game with me that requires attention (poker is fine) shows me that that person just doesn't care about the game. They aren't having fun, so they need an alternate form of entertainment. When it gets to that point, why even bother play the game in the first place?
Also, Amt does suggest a real theory. I have seen people pull really odd schemes to win a battle roads (a tourny that has next to zero prize support). What's to suggest that that cannot happen? Poker is much more regulated and they are very careful to ensure that this does not happen... but the pokemon staff is much smaller and less experienced. There is gonna be some guy some day who is listening to the opponent's hand through a cell phone.
Considering the older players make up the majority of the player base, it is important to keep them in mind. The "kid game excuse" only comes when people want to target older players with "old people humor" or marketing towards something kids probably won't be using (such as marketing the game through a bar... bad idea :3).
Judges have varying levels of comfort zones. The average plan here (where I live in NV) is allow watchers to be right at the table until the players shoo them away. I take every chance I get to make sure that all viewers are at least a table length away. Until I make that comment, you can be right over my shoulder and the NV judges won't really care. I know other judges are more strict, however. In California, we have a fine line about 4 feet away from the actual tables that you cannot cross. If you do, you will be warned. Considering that cell phones are VERY common, it is impossible to tell a judge to watch out for cell phones. Judges would be paranoid about cell phones in the tournament area. I have a program on my phone that reads texts to me if I get too lazy to read them. It is pretty easy to have people text me to give me hints as well. There are MANY possibilities in how to cheat like this. You only addressed a few.
I would like to know why you want this change. Does music help you think? Is it just to homogenize the rules with other games?