Granted, it's not going to make a difference for ~30 years but by allowing doctors to start younger means some of them will work as a doctor for longer periods of time. Most importantly your adding time at the end of their career when there most capable. (Perhaps add a specific associates degree as an acceptable alternative as even 1 or 2 years times a few 100k doctors adds up.)

As to reducing costs, undergrad is not free so if you reduce/remove that cost students can afford to spend more on other things. Start med school with less debt and being unpaid for the ~first year of Residency is more reasonable which means you could have more slots open for the same subsidy.

Still, I would also suggest modifying the billing rules. This may create some perverse incentives but it balances the costs between Medicare and private insurance while paving the way for increasing the number of available slots.