Actually, this sounds logical and fair. If one is going to enjoy the rights, privileges and immunities of citizenship, one should also bear the responsibilities. Registering for the Draft, if we ever have to resort to a draft again, is not an unreasonable burden to place on a young citizen.
In practice, I do not think our military services would have much use for drafted cannon fodder these days, of either sex. If the Selective Service were expanded to cover other forms of National Service in addition to Military Service, it might make more sense. If we ever NEED mass numbers of trainees to perform work for which there are not enough volunteers.
Actually, on reflection, I can think of a job for which we might draft both male and female citizen ‘soldiers’. Border Guards. The proposed (and under construction) Border Wall will need garrisoning and monitoring. 24 hours a day, 7 days a week of boring look out duty, with the sentries calling in the Border Patrol professionals if they see any incursion. Two years of manning the watch towers (like the forest fire look out towers of not so long ago) is not too high a price to ask a youngster to pay for the right to vote, and all the other rights, privileges and immunities of citizenship.
It works for Israel, it should work for us.