This would have no effect at all. It's only seems like a good idea for people with bad math skills or the people that wouldn't delete part of their holding which i assume would be everyone unless they were stupid. If you have 5% less total coins and the price therefore goes up 5% you are still in the same position.
If i owned 21mil bitcoins and they were worth $1, $21M. I then burned 1 million BTC so now effectively they are worth $1.05, x 20M still $21M. Market cap is what you want to see rising.
Not if the coins are not yours. What I am hoping is most only those with more than 1000 BTC would delete coins. I pledged 0.1 BTC deletion with only 10 coins. Businesses can say 5% of their profits can be deleted. I wish the protocol would be changed to delete all transaction fees but that is impossible.