This has been done before. Read about the London Blitz. Everyone there was pressed into service.
Being a draftee didn't hurt me. And, you are operating under the misconception that those who volunteer are only the ones qualified. That is wrong. It is training that makes one qualified. Whatever that might mean.
As an addition, my basic platoon was nearly all draftees. We set records at Ft. Lewis beyond what ever had been attained in the past. We excelled in all aspects of the training and because of our efforts the battalion commander was awarded at decoration for excellence.
I stand by position that the US mil should be all volunteer; unless in time of war. Your example illustrates my position - in times of war cops and firefighters were drafted, which I did not know. But no in non-war times.
And I am not saying that all or any percentage of draftees were not qualified. But in any draftee situation some (whatever percentage) will definitely not be qualified, especially in terms of attitude.