NIH likely funds 2/3rds of US biomedical research and ~1/3rd of global biomedical research by dollar value [0]. That link lists other big sources (ERC, MRC, US DoD, HHMI). My sense is that this landscape will change rather quickly with pandemic-inspired biomedical/defense initiatives and more private institutes in the US.
Moreover, NIH funding, due to its central role in supporting biomedical research, is often necessary for getting a tenured PI position. Many high caliber R1 schools require multiple R01 NIH grants for tenure. Often private funding sources are less valuable to universities because they pay lower indirect rates (<10% vs >40%) on sponsored research. As institutions are so dependent on NIH funding, the NIH can exert influence far beyond the research it funds directly.
Moreover, NIH funding, due to its central role in supporting biomedical research, is often necessary for getting a tenured PI position. Many high caliber R1 schools require multiple R01 NIH grants for tenure. Often private funding sources are less valuable to universities because they pay lower indirect rates (<10% vs >40%) on sponsored research. As institutions are so dependent on NIH funding, the NIH can exert influence far beyond the research it funds directly.
[0] https://health-policy-systems.biomedcentral.com/articles/10....