This feature request has been brought up multiple times on Meta Stack Exchange, and as far as I know it has always been poorly received by the community.
I think the main objection is that making high-rep users (even) more powerful is not a good thing.
I agree with many of the points made in answers to the MSE posts. For example, in this answer, devinb points out that
Reputation is NOT expertise! Reputation is [...] mostly [the product of] time spent on [a site].
You yourself have pointed out that trivial answers are often highly upvoted. This means that reputation has already been dealt out unjustly, yet you want to give high reputation users more influence.
This answer by Grace Note deals specifically with downvotes, but highlights what is for me the main issue:
The more egregious disconnect is the idea that high reputation users should have greater control on the reputation of other users. This would allow a small group of high reputation users to deal crushing blows to other users because of possibly minor effects. It greatly unbalances the system.
More reputation already confers more power (in the form of privileges). I don't want a more unequal distribution of power on the basis of reputation.
I also think vote weighting could encourage people to vote with the reputation impact of voting more in mind. Voting might be based less on the quality of posts and more on other factors like how much voting will affect others' reputation.
The purpose of voting is not to confer or diminish reputation, but to indicate which posts are the most useful. If reputation doesn't reliably measure anything besides time spent, that doesn't matter much (as long as the powers reputation confers aren't excessive), but if a post's score doesn't at least somewhat measure its usefulness, then the SE model stops working.