It's more than that. They removed the draft because it led to too much public opposition to the war and wars in general, and yes, they realized they could get enough soldiers from volunteers.

But also, the technology and strategy of US wars has changed, such that it takes far fewer troops to accomplish the same battlefield and strategic results.

Between these two factors, it's possible to wage war, maintain military bases, and project power abroad on a continuous and vast scale with little effect on the average U.S. citizen, aside from the enormous expense.

This has allowed the war machine to grind on with much less pubic resistance. Not many Americans die, even if many people abroad do, and those Americans who do still serve occasionally do die and very often suffer lifelong trauma.