You've acknowledged that the close reason is valid according to the FAQ, so your question seems to be one of whether or not the rules and general philosophy of the site make sense. While it's far too late in the game to be debating that point, I'll respond to it briefly anyway.
First of all, the very terse explanation for this is right in the FAQ itself:
Chatty, open-ended questions diminish the usefulness of our site and push other questions off the front page.
Questions that prompt a lot of answers and votes (beyond a certain point) are a bad thing.
As you've noted, it breaks the voting; people vote not based on the validity or clarity of the answer but on personal preference;
The more answers, the more the question gets bumped, again and again. Given the - as you note - high demand for these questions, it is obvious that if we permit them, a very high number will get asked, and since they also get answered (bumped) constantly, they genuinely will push serious questions off the front page - the kinds of questions that actually distinguish the qualities of Seasoned Advice from any other junky home cooking forum.
Recipe polls take no expertise of any sort to answer. Anybody can Google for answers and people actually do Google for answers. Look at the Margarita with beer question, or How do you make 'Rabri'? - both answered with pure Google keywords and no experience, and in the second case the person who asked the question was visibly annoyed at that. If we want to attract experts to this site - real professional chefs - we can't have a site full of questions that don't even take one second of cooking experience to answer (not to mention reward people for providing them).
And to put it bluntly, we would be providing an inferior service to those already offered by sites such as AllRecipes, Supercook, and the new Google Recipe Search. Our aim was never to duplicate those services but rather provide answers to the "long tail" of questions; the questions that aren't already easy to answer with existing tools.
Every social site - not just ours - will eventually devolve into opinion polls and lowest-common-denominator nonsense if there are no rules. In fact, this is such a well-known, well-observed phenomenon that it actually has a name, coined by Parkinson all the way back in 1957: Parkinson's Law of Triviality, more common referred to as the bike shed effect.
There is an inverse relationship between the relative importance and sophistication of a question or concept and the weight that is actually given to it. The more trivial the issue, the more accessible it is, the more attention it will get. People see the title of the question and their immediate thought is "oh, I can answer that one!" - and of course they see that somebody has submitted their equally trivial answer, and the net result is that somebody who - admittedly with the best of intentions - put no more than a few minutes of effort into answering a question that took no more than a few minutes to write, ends up getting nearly 25 upvotes and a silver badge just for being the first.
This situation is toxic to Q&A sites. It lowers the quality bar and leads to drama. It is, in fact, one of the very reasons that Stack Exchange (and originally Stack Overflow) was designed the way it was: To prevent obvious bike shed questions from taking up precious airtime.
Here on Seasoned Advice, since the very inception of our community, we decided that recipe requests are categorically bike shed questions and thus not allowed. It's as simple as that.
- Is there a demand for them? Absolutely, that fact was never in dispute.
- Is it possible for them to benefit some people? Maybe, sometimes.
- Are they good for the long-term health of the site? Not by any objective measure.
- Does that make us look "stuffy" to some people? Doesn't really matter.
We have clear, unambiguous guidelines for "culinary uses" questions. That one didn't pass muster.