Shouldn't we aim for conciseness and develop skills to articulate answers that say a lot with less words?
Of course you should always strive for conciseness. This is one of the number one rules of scientific writing—or writing in general if you want to keep your readers' attention. If I've learned something here, it's cutting out the irrelevant parts, or "bullshit", as you call it.
But you seem to be confused about two different dimensions, one being concise vs. excessive, the other being incomplete vs. detailed.
The former is the difference between merely explaining and explaining as well as saying hello, Merry Christmas, linking to your homepage, including a footer with your signature, emoticons, et cetera. The latter is what makes an effortless answer stand out from the rest, which leave no questions open, go beyond what's asked and are among the top posts on Stack Exchange sites as a whole.
Which brings me back to your first point:
Many answers I've seen are dauntingly written out like a college homework assignment when 2-3 sentences at the most would have sufficed.
Are you saying there couldn't have been two or three summarizing sentences? Why not? Many users like to put a TL;DR in front of their posts.
And if you think a post is missing precisely that, why not include it? There's an edit button below the post. For anyone. You don't even have to be signed in. Or, if you're an experienced Stack Exchange member, drop a comment. Ask for clarification or an example.
Finally there are topics that simply cannot be explained in a single line of code. I often found myself looking for solutions to programming problems, and—guess what—the one-liner on Stack Overflow really didn't help much. It was the answer that explained how the code behind worked and how the commands played together. Which made me learn something for a lifetime instead of just copypasting and forgetting.