I’d argue that the Vietnam draft did have a huge impact on the public reaction to the war. I think one of the reasons it didn’t have immediate political results is because affluent people (the kids of politicians) had many ways to avoid service, ie college or well known health excuses. I think if those loopholes were not in place the wide public backlash we saw would have been followed quickly by real political results.

Obviously this is speculation, but there’s logic in there.