Can't you even care to get the private keys of few of the addresses holding 5BTC? If you do this, I am sure people would feel more safe to play on your website. Its good for your business and if you are denying to sign a message with cold wallet addresses then surely there is something fishy about it.
No. I do not want to get something from these cold wallets before it is necessary. No player on our site can claim that he did not get any withdrawal.
Exactly the point, a player can deposit his own btc in the site and wins some and while trying to withdraw say 2 btc, you run with the player's money never to be seen again, the player needs to first know that you have sufficient funds to not ruin your "reputation" for a few btcs. Although it doesn't suddenly make you the most trustful site, it does reduce any hesitation from player to deposit on your site.