I have no particular view on the badge proposals except to say that they needn't be custom: they can apply as well to any Stack Exchange site. Rather, I'm mainly writing to disagree with the implied premise that it's always, or even as a general rule, appropriate to upvote a question one answers. Questions should include enough context that someone happening across them at any time can understand it; some questions on our site are about the weekly parasha (Torah portion) or upcoming holiday but don't indicate as much, giving no context. Questions should not include unnecessary jargon; some questions on our site (including, alas, some of mine) do. Questions should be written in readable English (when posted by a native, of course); some questions on our site are in SMS slang or in full-caps or without punctuation. Questions should mention the postulates (axioms) the asker is starting with, what assumptions he's bringing to the question (the relevant ones); some questions on our site do not. Questions should be polite; some questions on our site are demanding or dismissive. Questions should include mention of what work (including research or thought) the asker has already done toward finding an answer, if any; some questions on our site do not.
Any of these are reasons someone might downvote — or not upvote — a question. Even if he has an answer to it that he's willing to share.
Three additional notes closely related to the above:
- Note that the up arrow has the tooltip "This question shows research effort; it is useful and clear". The down arrow has "This question does not show any research effort; it is unclear or not useful". While people may upvote or downvote for any or no reason, those are, if you will, the official reasons for the votes. And, as I noted above, they can apply even if someone's answering.
- You say in your question "anyone who posts [e.g. an answer] is implicitly asking for reputation". Well, he might get reputation, but surely that's not the main reason for answering. People answer to supply information. Otherwise, (a) they'd never join the site (reputation's only meaningful to a SE user, not to someone considering joining) and (b) they wouldn't answer questions on meta (no rep accrues). So your corollary, that it's therefore "proper to grant reputation to anyone [e.g. the asker] who provided the soapbox" for the answerer to accrue that rep, is not all that strong.
- You say in your question "anyone who posts [e.g. an answer] is implicitly asking for reputation" so should "grant reputation to anyone [e.g. the asker] who provided the soapbox". Logically equivalent to that is that if the answerer is unwilling to upvote the question, he shouldn't answer. Really? Forgo providing the asker (and others) with the answer because, per my main point above (or for some other reason), he doesn't feel like upvoting?
And I have the same views, mutatis mutandis, about the necessity of an asker's upvoting answers he gets. (There, there's the additional counter that the answer may not be correct, or sourced, or the like, though not every reason for which one might not upvote a question applies to answers.)