I would go another direction with regards to a draft.
Military service required for all able bodied persons prior to attending any College/University if that College/University receives any funding from the government.
Those who are not able, or who for religious reasons can not participate can replace military service with civil service.
Make it a mandatory part of the admissions process. Mandatory for the schools as part of accepting government money. No one can attend that school unless they have served in some capacity. Draft the schools, not the individuals.
This way no one is required to participate. Even schools can opt out by not taking any government funds.
Make it a two for four. 2 years active (+6 IRR) for 4 years of schooling.
The military can stop spending any money on recruitment and that money can pay for school, either replacing or significantly reducing the cost of education for participants. The GI Bill could still be used for advanced degrees, or additional schooling.
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