I was surprised that Robinson won the poll so convincingly - yes, he was great, but no more than several other people on the show...
It can't say it really surprises me, since to a large extent a poll like that will be a tweaked version of a "which is your favorite character" poll. Garak is popular among fans of the show (with good reason), especially the more hardcore forum-going ones, and will therefore do very well in a poll like this.
Andrew Robinson's acting was certainly very good for the most part, but did not outclass people like Shimmerman, Auberjonois, Visitor, Alaimo and Meaney by any means. Brooks is more erratic, but at his best certainly deserves to be mentioned right alongside those others. Robinson is actually guilty on occasion of the kind of awkward pauses and wierd emphasis that Brooks is sometimes derided for.
Garak definitely benefited from only appearing when the writers had something important for him to do, as you say, and I tend to think that in hindsight Quark might have worked very well as a semi-regular for similar reasons.
With some other characters... it doesn't always work, you read the dialogue and you aren't as impressed as when you are watching the actor delivering those lines.
That's true. In the case of Quark, this is a character who is very well-written as part of the ensemble, but who then has to struggle mightily with some really bad material in his own episodes. It's a pretty unique case in that sense, perhaps somewhat comparable to Jadzia, but more extreme. There's a whole litany of very mediocre to outright bad episodes that Shimmerman is forced to carry: Family Business,
Prophet Motive, Bar Association, Ferengi Love Songs, Profit and Lace, etc. Shimmerman seldom got the material he deserved in the Quark-oriented shows.