Comment by wahern

There are no artificial restrictions on residency slots. The Federal government funds a fixed number of slots, but states and hospitals also fund residencies. The "shortage" has much to do with geography and specialty--the money and interest is working in specialties on the coasts, not as a GP in rural towns. People who are rejected are typically vying for slots in high-demand areas and specialties; they often could have been accepted if they had applied elsewhere.

One answer would be to raise GP salaries, but that's difficult, especially if you're self-funding residencies and already paying out the nose for specialists and other inflated expenses deemed necessary in modern healthcare systems. Kaiser California imports medical school graduates from abroad for their in-house residency programs, which is presumably cheaper than raising salaries to draw more US resident candidates.

Kaiser arguably points the way forward. As an HMO--a vertically integrated healthcare system--there's greater financial incentive to self-fund residencies. When insurers, hospitals, and doctors are all at arms length from each other, the financial incentives don't align very well, thus the "need" for outside funding (i.e. the government) of residencies.

Note that unfunded residencies are also a thing, where the resident is responsible for sourcing the funds for their salary and expenses.