If you make it more difficult to enter a review, your quantity of reviews is going to drop off. You are also more likely to get only the most passionate responses. The majority will be people on a mission to get revenge for a bad stay. You might have a few that really loved it and want to promote the business. The middle of the road people are going to be the "meh, too much hassle" group that just stops reviewing.

Amazon is easy since you order, pay and review on the same site - so they can easily link, and the computer can do it without need for human intervention. Since you can't really book on TA, you would have an extra step of scanning/faxing your receipt and someone actually verifying that it is not forged and the dates match. Much more labor intensive and costly - especially for a company that is only making revenue off of advertising vs. actually selling a product like Amazon.

Not sure that Facebook integration help either. I refuse to link my FB page to my TA or any other site I participate in for general recreation or amusement. It is also not difficult to set up a fake FB page, so the issues remain.