The cyclist's equivalent of h is E, the Eddington Number.
the largest integer n such that one had cycled at least n miles on n different days.
It is painful in both cases because it's a measure of reliable work, not most overall impressive work. If you write 16 papers and 15 of them are cited 15 times and one is cited 2000 times, your h is still 15!
Maybe an alternate distribution would be some number n such that there is one paper cited at least n times, at least two papers cited n/2 times, at least 3 cited n/3, up to n=10 or so. Allows for a bit of a tail and still easy to remember and calculate. Could dramatically shift weight toward people publishing multiple landmark papers.
What will the keepers of this index say to the social justice criticism that it's unfair to track this metric because it discriminates against women and minorities who don't get chances to publish as much?
I'd say it's a good way to measure discrimination, among other uses. If the average h-index for a given group is significantly lower than other groups, it could indicate a discrimination problem. Ceasing to measure the problem won't make it go away.
http://www2.lowell.edu/users/jch/mtb/e.html