There actually is a pay them more button that the federal and state government controls, but I doubt they'd hit it. Many of those rural docs are compensated heavily by Medicaid (EDIT: have a high % of Medicaid patients - compensation is a separate story), but the reimbursement structure often penalizes those rural docs vs. those that take positions in suburban and urban environments. Some states permit a flat reimbursement structure where patient volume is the only difference, but other states further penalize the rural docs by "shaping" reimbursement rates such that more funding goes to the urban and suburban areas.
This administration could address that, but if anything, they seem to be moving in the opposite direction.
Rural medical specialists are compensated very well. In my experience the bigger obstacle to getting those roles filled is more social, for example, unless you are already married the dating pool in a rural area is a consideration for new doctors, or if you are married and your spouse has a career moving to a rural area may require them to give up that career which they may not be willing to do. Cities better support dual-career households b/c they have a density of industries. Also - after 10+ years of school a lot of new doctors want to live it up a bit in a place with things to do and see.