I key difference and qualifier is a private company CAN have the same amount of waste but not necessarily and like modeless mentioned, private companies can fail and we can move the services to another.
It's guaranteed the federal government is going to have waste and be very difficult to change because you cannot let it fail.
Why do we need to stamp out "waste"? A bit of waste is inevitable, and is human. Excessive waste, sure. But I think Musk's DOGE goal is to stamp out all waste to 0, and that is simply impossible.
For example, the only way not to waste any food whatsoever, is not to eat. It is inevitable there will be some small portion of food wasted.
Chasing perfect efficiency is a fool's errand, since humans are not perfect.
It's guaranteed the federal government is going to have waste and be very difficult to change because you cannot let it fail.