I think there is a difference between users who ask a lot of questions and users that are border-line spamming the site.
I hesitate to use the word spam because it implies malicious intent. But there are plenty of questions that still feel like the user was more interested in getting attention then in solving a problem. There are definite examples of spam like "How to for getting the gurls on the intrenets?" (actually, this may fall more under the category of vandalism), but there are also plenty of questions like "My form doesn't work" or "I want the pictures to be embedded into the PHP." Questions that are lazy, use poor grammar (and obviously not due to ESL), or don't bother providing any examples are very close to spam, I think. They don't show that any time was taken and they show a lack of courtesy and respect for the site and other users. This sort of behavior should be distinguished from that of users who ask more than answer, aren't bright, can't learn, won't learn, or just want to use this site to do their homework.
I make the distinction because I ask more than answer (last time I checked). I also answer without being sure of the answer. I also ask without researching my question elsewhere thoroughly.
I am, at best, an autodidact when it comes to computers and programming. I don't understand best-practices, I've taken one CS class (intro, got a C), I am guilty of using tables instead of CSS (but that was back in the bad-old-days) and of using arrays where objects would be better. I have read more than one site on OOP and just don't get it. I don't get JSON at all. I use the term Web Service when I mean SOAP. I do things by hand because I don't trust libraries.
And I try to only ask questions that I think need an answer.
My friend gave me crap once when I mentioned how I ask a question on here nearly everyday whenever I get stuck. "Oh, you're one of those users..." he said. I was embarrassed by saved face by pointing out that a majority (or solid minority) of my questions get up-voted. Someone must think they worth asking, I told him. But the more I think about it, I think my embarrassment and his resentment was rooted in this ugly trend in the IT world of grouping all helpless people together. "One of those people" is a collection of anyone who asks a question that experienced and formally trained programmings take for granted AND users who ask lazy questions like "How can I make my text a different color?"
So as a user who asks more than answers and who feels under-qualified to try to offer my limited knowledge, I can appreciate the spirit of this question. I don't think the problem is with users who leech answers without giving back, it's with users who don't appreciate the community enough to take their when composing their question and take their time in deciding whether they need to ask the question at all. (And we end up paying for it because it takes our time to read it and piece together a possible response).
To the notion that limiting questions limits those answer questions, I agree unless someone gets credit for giving an easy answer to a bad question. By not accounting for this, we allow for inflated reputations that only reflect lots of answers, not lots of good answers.