SPOT ON...you really nailed it and in the fewest words possible.
Of course part of the delusion is that there has never been a time when everyone served. Never.
There was never even a time when all males served.
No, not even World War II.
When you have a population the size of ours there is no way a "no exceptions national draft" would work. The 3.5 million number is how many young people graduate from high school every year. To have a system that would take that many people in every year, train them, feed them, house them, clothe them, would be a system that would be so enormous that it would run the country.
We would at any one time (assuming two years of service) have 7 million draftees in the military would have to be 10-12 million. Considering how much fuss is kicked up about the military budget every year (between four and five percent of GDP) does anyone think a growth of 1000 percent would be greeted with cheers?
40 to 50% of the national GDP being spent on the military is as much or more than we were spending in WWII.