If there were marginally less research funding, the research program cancelled wouldn't be chosen at random, it would be the least promising one.

Ah, right, we're on the same page now. Your argument, however, assumes that a) fruitfulness of research is quite highly predictable in advance, and b) available funds are rationally allocated based on these predictions so as to maximise fruitful research (or the proxy, citations). Insofar as the reality diverges from these assumptions, the expected number of citations of the "marginal" paper is going to approach the average number.

Note that I did not say that papers, on average, get no citations. I said that the average (I.e. median) paper gets no citations.

Oh, by "average" I assumed you meant the arithmetic mean, since that is the usual statistic.