I think for Republicans specifically the reason they would support the draft is because it's your patriotic duty. Trump's reasoning was not enough people are signing up for the military. Never mind that patriotism might be low due to who is in office LOL.
Ayn Rand vehemently opposed the military draft, calling it "the worst" statist violation of individual rights and a form of involuntary servitude. She argued that forced military service violated a person’s right to their own life, advocating instead for a fully voluntary army. Rand maintained that if a war is just, men will volunteer, and if it is not, a draft should not compel them.
Moral Objections: Rand believed that forcing individuals to serve in the military is an "abrogation of all rights". She argued that a government's role is to protect rights, not destroy them by treating citizens as property of the state.
Voluntary Army: Rand advocated for a volunteer military, arguing that it is more effective and consistent with a free society.
The Draft as "Statism": In a 1967 talk, she claimed the draft establishes the principle of statism—that the individual belongs to the state.
Critique of Vietnam War: She believed the draft made immoral, "senseless" wars like Vietnam possible, as it allowed foreign policy adventures that citizens might not otherwise support.
"Rights Impose Obligations" Myth: She rejected the idea that rights involve obligations to the state, viewing that argument as a way to turn rights into a gift from the government rather than an inherent, individual possession.
Rand's position was considered unique during the Vietnam era, as she attacked the draft on principled, moral grounds rather than simply pragmatic or political ones.
Maybe Rand's best line on the draft: a right to a paycheck but not a right to their life.