The number of residency slots (a legal requirement to be a doctor) is limited because it's funded by Medicare and only Congress can increase it. AMA (American Medical Association) has lobbied to keep it that way.
not really, but private funding is generally pretty controversial with weird incentives (e.g. a company may only fund for positions that will create demand for their products--like a skincare company only funding dermatologists) [1]
don't think many other entities besides the federal government have a ton of incentive to fund residency. and the federal government does have caps on residency slots
they contribute already, but it's more challenging than federal. many residents do not stick around in the state they train in, so states have less incentive to fund this