Some private foundations do charge less, but they’re usually not providing the bulk of the funding for a given lab. There are generations of researchers and American industries based on the model where NIH/NSF provide a stable foundation for research, and while that can change it’s incredibly disruptive to try to break existing agreements.
To put it in HN terms, do you know anyone who take lower paying non-profit work because they’re married to someone with a tech job which means they never worry about their mortgage or health insurance? This is like that spouse’s employer saying they’re getting a 30% pay cut.
When looking at the whole system it clearly becomes woefully inadeqate. To extend the example, the only direct costs of an airplane flight are the crew, the fuel/food, and any airport fees. Could you run the rest of an airline (training, ground staff, scheduling, booking, IT, maintenance) on 15% of the crew+fuel costs? Not even close.
If you look at federal contractors and other companies, the overhead on staff is probably closer to 100-200%, so 50-60% is very defensible.