For perspective, the CS programs in the NSF already have a two-submission limit per year [1].

Besides reducing the incentive to spam, this rule has had another positive effect: As a researcher without funding, you don't have to spend your whole year writing grants. You can, instead, spend your time on actual research.

With that said, NIH grants tend to me much more narrow than CS ones, and I imagine that it takes a lot more grants to keep a lab going...

[1] https://www.nsf.gov/funding/opportunities/computer-informati...