The people who need to evaluate academics (both individuals and institutions) for purposes of funding, promotions, tracking goals, etc, can't really do it well on their own (you need to have domain-specific knowledge to be able to pass independent judgement, you can't have domain-specific knowledge in all the disciplines you need to manage, and you can't/don't trust self-evaluations) so they need some independents oracle that gives any metrics that are at least roughly correlated with output and quality even if they inevitably get gamed; and it needs to be something that can be independently evaluated cheaply and simply, so that it can be written into some formal criteria and there won't be a legal dispute whether a research outcome is "sufficiently good" or not, or whether applicant A has "more points" than applicant B on some objective scale that doesn't put the burden of personally proving that on some official who realistically can't do that anyway.
Publishers, prestige of publication venue (including their ranking in citation metrics), indexes like Web of Science/Scopus/etc all provide this function to the administrators of scientific funding, who want (and need) to evaluate academic prestige.
The other need is for a filter to allow a researcher to not access most of what is published. There is generally a problem of too much "research-like work" that is impossible to read all of what gets written, so researchers want a filter system where someone else throws out at least some of the crap (or forces the crap to be re-written to be better) so that there's a better signal-to-noise ratio. In the current system where there's motivation to publish in "better places", if something is published in a "worse place" that's some evidence that the paper is weak (because if the authors could have published it in a better place, why didn't they?) and thus perhaps can be discarded without reading, or deprioritized to read only after you've read all of the better-ranked stuff.