Your thinking is a bit backward from the logic applied. The argument is that the draft is used, first and foremost, to fill the combat arms roles required in a major war. Therefore, if one is ineligible to the combat arms, one is not required to be in the draft.
From my memory (which may be suspect), the “include women” argument was really used as bait to try and get rid of the selective service altogether. The anti-drafters thought including women would scuttle registration. But their arguments were rejected because women cannot fill the primary roles sought in a draft.
The “plum role” part comes in the volunteer army, where combat arms are considered a distinguishing role, so that officers and enlisted who serve there have a leg up in the race for promotion.
Is my thinking really that backward? In today's military, what is the ratio of supporting to combat roles? I think it's pretty significant, and good deal higher than one to one. In a situation where there was a general draft, there would be plenty of danger to go around, and not just for combat volunteers.
I agree that many military volunteers do consider combat to be a job they want, but I'd submit that in a mobilization, many draftees would prefer not to get that job.