Why 7 days and also have to prove you contacted the winner?

I quite agree that as GA creator you shouldn't be forced to do any extra work if your GA is not redeemed within 7 days. If possible it should trigger an automatic re-roll.
I had to contact some of the winners of my earlier GAs via e-mail in order to ask them to activate their keys or tell me whether there is some issue. While it doesn't involve a lot of time, it still feels like an unnecessary step for me to take to do something nice for others.

I learned that using whitelist and groups mostly eliminates that issue, though. Which is why I keep adding people to my whitelist if I feel they are decent people and/or they have a nice Sent:Won ratio. As happened in this thread. I quickly check people's profiles if I think they show a basic command of social interaction and unless they have abysmal ratios, they go on my whitelist. I prefer giving games to people who have shown their support and interest for SG than to those who never participate in any way and simply are here to win games.

Also, I usually do Level 3+ (or higher) GAs, as the chances of coming across ignorant people are much lower.

The one thing I won't let this rule do is to keep me from creating GAs. Neither should you. :)