I inferred from this that the community does not want such comments posted.
Well, it's a bit more than that.
The design of Stack Exchange grew out of a frustration with traditional forum / message-board / newsgroup discussions.
Not because they don't work to solve problems, but because extracting the results is so tedious. Rarely does anyone go back and summarize a back-and-forth discussion; future readers must (if they can find it at all), trudge through the entire conversation, gleaning tidbits of useful information like so many wild strawberries scattered along a mountain trail. Which is quite a relaxing activity, provided you're not very hungry.
Oh yeah, short thankyou comments...
Well, so this desire to build a tool for organizing information in structured Question + Answer format ran into a bit of a hiccup early on: sometimes you need a bit of discussion. To clarify what's being asked, or hammer out the finer points of an answer. So comments were added.
...and immediately blew up. Wasn't long before there were posts with dozens, scores, even hundreds of comments attached, tangential discussions and critical critiques mixed together like a strawberry-and-olive milkshake. This wasn't working.
So a few changes grew up over time, with the aim of suppressing non-essential commentary:
Lengthy comment threads get hidden. Only the first - or most-upvoted - comments get displayed by default. This is why voting on a helpful comment is important, in particular if you can't edit it into the post in some form: an up-voted comment will rise to the top of the pile where it can be quickly accessed by future readers.
Very short comments get blocked. "Thanks!" may seem very friendly and personal, all there by itself. But once they start piling up, they're just more scrolling. Of course, this is perpetually controversial, since it's always other people's comments that are annoying or noisy. When I write "Thanks!", it's a masterpiece of modern literature in one word.
Flags for noise. Desiring to keep those most relevant comments quickly accessible, some folks started looking to clean up comments that had served their purpose. So the flagging system for comments was expanded to include off-topic, obsolete and "too chatty" options. Note that comment flags - unlike normal flags - don't impose any penalty, leave the flagger anonymous (even to moderators), and don't leave any sort of negative mark on the profile of the comments' author; they're just a quick way of getting non-essential comments cleaned up.
So then what can you do to express gratitude?
Well, you can cheat - either by padding out the comment in a way the system doesn't detect, or just making it more verbose; "My utmost gratitude to you good sir for your excellent response!"
But you're probably here to trade knowledge rather than social niceties. So in a sense the most sincere "thanks!" for knowledge gained is giving a little back... Whether that's telling the person you're thanking why his words helped you, or passing the knowledge gained on to someone else - and crediting its source.