This is often not true, and if it was true it would be backwards.
Funding bodies also employ academics who are able to judge the quality of proposals or they solicit feedback from experts. You don't just write "I've got a bunch of first author papers in Science so you should fund my grant." This is important because if the only thing that funding agencies use is institutional reputation then we end up with an even larger percentage of funding only going to entrenched academics at a very small set of institutions.
I'm seeing KPIs for grants (and even for the whole programs of grants) as, for example, quantity of publications in top quartile impact factor according to e.g. Scopus and Web of Science.
They do not want to evaluate each publication separately or pay experts for a separate review of each publication (if they would, that could be a source of funding proper peer review instead of it being done by random volunteers) but rather defer to the existing ratings of the publication venues. They need a simple objectively measurable quantitative metric, not a complex qualitative one.
Funding bodies also employ academics who are able to judge the quality of proposals or they solicit feedback from experts. You don't just write "I've got a bunch of first author papers in Science so you should fund my grant." This is important because if the only thing that funding agencies use is institutional reputation then we end up with an even larger percentage of funding only going to entrenched academics at a very small set of institutions.