Having the citation's impact on one's H-index decay with author position would cause an interesting stir to the "academic game". I wonder if we would start seeing supervisor's bully for first authorship.
(My name moved from the end of the alphabet to the middle when I married. I was amused that it actually makes a difference).
The worst thing to have is indicator counting of any kind. The system will be swamped with mediocre, sometimes almost fraudulent scientists who game it. (It's just too easy to game the system: Just find a bunch of friends who put their names on your papers, and you do the same with their papers, and you've multiplied your "results".)
H-Index is also flawed. In my area in the humanities papers and books are often quoted everywhere because they are so bad. I know scholars who have made a career by publishing outrageous and needlessly polemic books and articles. Everybody will jump on the low-hanging fruit, rightly criticize this work, the original authors get plenty of opportunities to publish defences, and then they get their tenure. Publishers like Oxford UP know what sells and are actively looking for crap like that.
A tool which was used to resolve issues among chemists and biologists is now running rampant over fields which do not have a high volume of citations. Mathematics is suffering, for example.
An Annals of Math paper might have fewer citations than a paper in Journal of Applied Statistics. But the prestige is incomparable.
This is purely by convention.
part of this is contingent upon citation formats used in different kinds of publications (and thus different fields) where long lists of authors are condensed to one two or three at most.
this is not even getting into more locally scoped, second order inputs such as any given department's traditional handling of advisor vs. grad student power dynamics.