That makes alot of sense, we need more than anything else, users who will come here to read good content and will stay here to support their favorite authors/bloggers/writers etc.
The incentives which are an additional feature, if managed properly , can propel steemit to being as big as reddit, quora and the others.
We do need to do something about the influence vs reward link. I think the solution would be make reward less proportional to influence/Steem power by including a formula with a smaller coefficient ration. In addition to the upvote button, a content rating button between 1 to 10 should be added strictly for rating content based on quality. This add feature should have more influence on rewards. However an upvote's influence on publicity does not need to be altered. In a way we cannot remove the pay for publicity mechanism which I think would be huge for steemit's self-sustainance in the far future.
With the above changed, increaded publicity would not necessarily mean greater rewards than a blogger who for example, has a content of higher quality.
What this will create is incentive for higher quality content.
To summarize the above (might have explained with a bit of complexity and lack of order), rewards should not depend fully on the steempower or influence of the upvoter but more so on an additional content rating feature.
I really like this idea of yours, this would give more value to one's reputation. I agree the trending page is dominated by a few Steemit brass, hopefully this is the product of a very small user base right now. Personally I scroll through new posts on a selected tag, I wanna see everything but yes there is a lot of crap posts.