Interesting idea.
My first thought on this is that it would require too much effort to get it set up where you're only voting on the authors or types of content that you actually like, to the point that people would just give up and this would create a different type of problem -- no one would be voting and everyone would be getting the same number of tokens per payout...and what's the value in that?
I think it would be interesting if someone could code a browser to track the number of seconds spent on Steemit posts and you can set it up within the browser to automatically vote on each post with your time -- the more time spent on the post; the more attention that you give it, the more you pay out to the post.
It would be nice if we had the option within the browser settings to spend all our voting power up, down to a set percentage (say 80%) every day, which will make it look back at how much time you spent on each of the posts and spend the appropriate (proportionate) percentage of voting power down to 80% (if that's the value that you settle on). However, I believe that there should also be a cap on how much voting power you can spend per account, regardless of time spent on that account's posts (say at 5% daily voting power).
In other words, if you spend a total of 10 minutes on post A, 20 minutes on post B and 30 minutes on post C and you have your browser set up to spend all your voting power down to 90% (use 10%) per day, then you will have 10% total to pay out for a total of 1 hour spent reading posts (having a post open in a window), or (10/60 minutes) 0.167% per minute. This would allot post A (10 X 0.167) 1.67%, post B (20 X 0.167) 3.34 % and post C (30 X 0.167) 5%. If C had been open within a browser window for say an hour, it would still only receive 5% of your voting payout, because that's the voting limit allotted per account.
To deal with having multiple posts open at once, the program will pick the first post that was opened and highlight that window in some way (say circling it with a flashing green border), which let's you know that you're only currently paying out (with your time/ attention) to that post. Once that post is closed out of, or that tab is closed, then the next window will become highlighted and you'll start paying to that post.
You may also have the option to decline payout to a post, presumably because you don't like it, by ticking on that option on your browser or within the post itself. So, this kind of follows your idea where you have to vote not to vote in order to not spend your SP on the post. It assumes that the post having your attention means that you like it and gives you the power to state otherwise with a simple click of a button.
This way you pay with your attention. In other words, you suffer for voting on content that you don't really like and you're further incentivized for spending time reading content that you do like.