I have no idea about "majority" either, but we are occasionally discussing what a "fair metric" would be for counting publications. Everyone agrees that the evaluation of the true scientific merit is impractical (or even impossible) for a variety of reasons from impossibility to carefully read and evaluate all papers in a variety of completely different areas to the mere fact that to estimate a true impact of something, one has to wait for 10+ years at the very least.
Our current system (as far as I remember it) is to have tier 1 and tier 2 journals with 2 points for a publication in a former and 1 in the latter (there are also some fancy rules about sole publications vs. co-authored ones I was too lazy to read properly, so I'd rather skip them here). It is far from ideal and is constantly critiqued from all sides, but it is a not too bad compromise after all. I've heard of much worse arrangements where the formalization was brought to something completely absurd (from my perspective, at least). The tiers are determined by "general agreement" (and there is some fight here) with the impact factor playing some role, but not the decisive one. In general, it is believed that the individual citation metrics (like h-index) reflect the true impact of a researcher much better than the sum of journal impact factors times the number of papers in that journal.
The main reason for the very existence of this point system seems to be that neither we would like to explain to the administration what is worth what on the routine basis, not the administration would like to hear such explanations more often than absolutely necessary, so everything should be reduced to a single number. When really important cases arise (like promotion to tenure, etc.) the number merely needs to be above a certain (fairly low) threshold and the decision is made based mostly on the recommendation letters and such, but for trivial issues like annual merit salary raise that number suffices and everybody can see how the awards are made. Transparency here is at least as important as fairness and since the latter can be hardly achieved even in theory, resorting to the famous KISS principle is a reasonable idea. As long as the point system (whatever it is) doesn't acquire life and power of its own that overrides common sense, it is harmless and even useful.
Of course, the situation varies from place to place, but what should be remembered is that many rules like that are not creations of the universities, but rather of the faculty in the particular departments, and the ugliest monsters are born when people do not want to agree on anything or even to listen to each other. Various "rankings" by independent agencies also play some role, of course, and the citation factors play noticeable role there, sometimes in a rather weird (again, IMHO) way.
As I said, the current system is far from ideal, but if you ever come up with a bright idea of a really good way (fair, transparent, and practical), let me know and I'll be happy to advocate for it locally :-)