My parents were very much in favor of the wars. They also were 100% adamant that I could not join the military.
With national service, that choice doesn't really get to get made. I feel that over the last 10+ years, the wars were out of sight and out of mind for a lot of people because their kids weren't at risk. I feel like the questions would have been a lot harder on the gov't if we still had a draft going on.
Interestingly, the US armed services absolutely 100% do not want the draft. They get less oversight without a draft. The all volunteer force is higher quality and there are fewer issues with people going AWOL, and people are more likely to stick around so training costs are lower. I think the people that don't want a draft are those that could be drafted (totally understandable, I wouldn't actually want to go to a war myself), and those that like their wars without having to deal with the costs.