For a basic tl;dr, scroll down to the image in the middle of the answer...
Downvoting legitimate questions on Meta because one disagrees with the question's premise has become a bit of a problem.
Agree totally
From my 2nd/3rd week here having become a bit more familiar with everything I noticed the less-than-ideal double usage of the voting system on Meta.
As the two usages of the voting system are for entirely separate requirements, the votes are almost meaningless as the two are mixed. While sometimes obvious, you cannot always determine if people are voting to agree or disagree with the idea/proposal etc or because they felt the question was bad.
Voting is based on personal opinion/reasons, and even when the voting system is for a more single set of purposes (such as SO), with the personal judgements, "out of bed the wrong side" and "had a great day", one can only summarise to a certain degree of accuracy what and why others have voted.
With Meta votes having two purposes, it's even harder to judge, sometimes not possible.
However, currently it's the only quick and simple means to agree or disagree.
Reasons it wont work
Vote on the question based on its clarity and usefulness, and express your disagreement in an answer and allow your opinion to be voted/vetted by the community on its own merit
This would of course work perfectly, without doubt... if everyone adhered to it, but first they'd have to know about the change, and even then, how many people will actually change?
- People stuck in their ways can't be bothered to think about something
new;
- They forget about the change;
- Are stubborn, simply wont be enforced or persuaded to change;
- Like it the way it is/disagree with the change;
- Too much work to now have to answer or wait for an answer to voice their opinion;
- Too much work to read the question and additionally answers to be
able to vote based on agree/disagree;
If there is no answer for people to cast their vote on, are they going to return later to see if there's an answer? Or post one themselves? Not everyone answers, but lots of people vote!
Even if there is an answer, the answer content/context may not directly reflect either their agreement or disagreement of the original question. So they still don't vote, or may vote falsely/inaccurately, or again just vote on the question as it's always been.
As you never know who's voted (or why), and in any public community people do all sorts of things for weird and personal reasons, many have no reason to change and can continue the way it is without anyone knowing.
Of course you could promote the change heavily and so only a few vote incorrectly, but still, Meta is unique in that people vote purely on their opinion of a feature-request or suggestion.
So while I like the "vote on answers" idea, it's still not ideal for the aforementioned reasons, and I think as Meta is Meta and agree/disagree is a large part of this site, it should have a specific function to handle what is a good percentage of its purpose.
I know only two well the issues and requirements with a new function/feature, and I can see this one scaring the whatsits offa people here. But if you want to have two separate purposes of voting on meta that works well and people understand and don't have to do much work with, they're simply going to have to be separated.
Suggestion
Have a secondary voting mechanism for questions and answers right under the current one. Both labelled clearly so people know what's what.
Top one: Standard Clarity/etc voting;
Bottom one: Agree/Disagree;

The good thing about this is you can have it on the question and vote on the idea without having to wait for an answer that suits your opinion to vote on.
And when answer do come along you can also vote on them as to whether you agree/disagree.
I'd say agree/disagree votes do not change your rep at all, they're literally just a vote count for the given question and answer. Although I suggest a min rep requirement on Meta of say 500, to stop people voting who don't yet know enough about stack etc.
I don't know the best structure for this obviously, and it should be considered if this would only be on specific tags, or create a new one to handle this "proposal" tag. If you want votes on opinion and agree/disagree use this tag.
(I can feel the site's devs hurtling towards my house now...)
Discussion can be suppressed. Heavily downvoted questions fall off the front page, and no longer have any visibility.
This is another really bad result of the two voting requirements being mixed. With my above proposal, this would no longer be an issue.
The top voting would be as per normal, rubbish/dupe questions would be voted off the page.
Good question would remain, regardless if people strongly agreed or disagreed.
Returning the natural order of things where questions are placed based on question merit.
The new feature provides potential consideration for factoring in both the question "clarity" votes and "agree/disagree" votes somehow for question placement. ie if a question is rubbish and not many agree, it's pushed past those questions which have a few upvotes for well presented etc and a few people agree.
If this has the (likely) affect that new questions push the older ones away and lack of visibility causes no more votes, when there may otherwise have been a lot of "agree" votes, then bounties become more useful!
The ban/enforcement algorithms would also come back into play as they have their own vote counts, although still less harsh as other sites/areas.
An idea I had to work in addition with the secondary vote mechanism:
Consider new tab(s) (ie where "newest" "featured" "frequent" etc are).
Perhaps have "feature-request" and/or "discussion" tabs for all questions with tags of the same name.
This would collate all questions which are more about agree/disagree votes, and so factoring in both the question "clarity" votes and "agree/disagree" votes for question placement would be better suited too.
Just a thought..