When releasing the ponh prototype we opted for a questionnaire at the end with a few questions and then a free form comment box at the end like you suggested. Right now theres over 1400 replies.
I doubt we'd get that many emails. And I seriously doubt we'd be able to use the emails in a similar manner to get the answers to the questions we had.
http://www.exitstrategyentertainment.com/ponh/?p=284
But think of it in games design terms. You need to streamline the process so the player does what you want him to do.
If you provide an email the player would have to
1. copy the email
2. fire up his local email program (or go to his email account in his browser)
3. paste your email
4. then start typing about his personal experience. Where would he start?
5. send it in.
Whereas having a questionnaire pop up at the end:
1. fill our the parts he wants
2. send it in
and it would be anonymous.
The problem is also that you'd actually rather hear from the people that hated your game, and more specifically what they hated about the game. If you make it to hard for them to do that they probably wont.
Being the only game I played through multiple times (never found all the hearts 
)
