To answer the question in your title of whether there are any good reasons to use Quirks for a new site - no there aren't. Standards greatly increase cross-browser compatibility, making development much easier and faster.
To answer your question of why a site like Amazon uses Quirks - firstly, they aren't new (their first sale was in July 1995), and secondly, it's probably not cost effective for them to change.
Unfortunately, good quality standards haven't been around throughout web development history. A site as old as Amazon is likely to have needed hacky tricks to make everything work up to this point, all of which would have to be rewritten. As JamesRyan says, it's a lot of work to update an entire site to use standards. A part of this is updating code, but I'd argue a more significant part is in time-consuming testing. Then there's the significant risk of lost income due to introduced bugs, which would affect revenue and in serious conditions, market value (probably only temporarily).
Amazon works, and works pretty well. Considering that and the risks involved, how do you think the business would justify making the site standards compliant, when it would mean average Joe User miss out on new features that will gain Amazon more revenue?