It would lead to the US military becoming way too large, and given the prowess in media propaganda, you'll get tens of millions of people with a highly militaristic mindset with nothing to do - think current soldier worshipping x10.
I disagree. The current volunteer-only military service means that only people with that mindset join in the first place. If there were compulsory military service, that would mean everyone else, regular people with no desire for glory/etc would be in there too. Look at what happened during Vietnam. There was such drastic anti-war sentiment specifically because anyone could be drafted.