The argument (already being made) is that it would weaken the military, or weaken military effectiveness. The fact that the combat forces are successful with a relatively small percentage of volunteer women does not imply that they would be equally successful with a much larger contingent of conscripted ones. Given that this battle seems to be engaged already, I will be surprised if it doesn’t make it’s way up to the Supremes.
As for not having a registration, I think it would leave too much potential for people to slip through the cracks and lead to a bigger perception of unfairness than is inherently present in the process already. If the possibility of a draft, however horrifying, exists, then registration seems like the fairest approach. And yes, it should include women.
My husband is a retired military officer, so I have seen various sides of this issue. The one thing that I do know is that they keep the draft because it is easier to have the structure in place and not need it. If they dismantled the draft, it could take time to set it up again.
I have 3 daughters and I would not have a problem if they would have had to register for the draft. It is only fair. I fervently hope that the draft is never needed again, but I am okay with it still being in place.
https://www.thoughtco.com/selective-service-system-and-draft-3321281 is an article about options relating to keeping the SSS as is, reducing it to “deep standby mode”, or deactivating it entirely. The ongoing costs, and the time needed to supply inductees in a theoretical draft activation:
Keep SSS as is: costs $24.4 million per year (GAO); can begin supplying inductees in 193 days (SSS)
"Deep standby mode": costs $17.8 million per year (GAO); can begin supplying inductees in 830 days (SSS)
Deactivate SSS: $6.5 million one time cost (SSS), then $0 afterward (GAO); can begin supplying inductees in 920 days (presuming that a new SSS or similar would be created in the event of a draft)
SSS also says that having a draft in the latter two cases would cost $465 million, but there is no mention of the cost of having a draft with the current SSS as is.
Note that, in addition to the time it would take the SSS to supply inductees to the military, the new inductees would have to go through seven to twelve weeks of basic training, then any applicable job-specific training, before being able to do whatever jobs the military needs them to do.
That argument confuses registration with classification and conscription. In the event of an actual draft, then the selective service would classify registrants and nothing precludes them from modifying or refining the classification system depending so as to better fulfill specific needs. Not everyone who registers will be drafted. If anything, a larger base of registrants to draw from can only strengthen military effectiveness, because the selective service could develop more a more targeted conscription system to ensure that necessary roles are filled.
Several years back, H’s workplace (fed govt) did ask for volunteers to see if folks wanted to be deployed. Most of his workforce is in its 40s and up but I think there were a few volunteers. It can be challenging finding the right match of fitness, skill set and willingness among volunteers, especially when they’re older.
Also, there are age limits for entering US military service. The statutory age limit is 42, but each service can set a lower limit (currently ranging from 27 to 39, according to https://www.usa.gov/join-military ).