Unless you have popular support behind you, a draft is a great way to make your military less effective. You get a bunch of soldiers who don't want to be there, who may not do their job to the utmost either out of apathy or active malice. It also gives lots of people, who might otherwise passively disagree with your war, a great incentive to actively resist your war and your attempts to force them to fight in it.

It worked in WWII because of Pearl Harbor and the Axis being cartoon villains. Direct US involvement also only lasted 4-5 years. Vietnam demonstrated that an unpopular, long-term conflict is ill-suited to the draft.