To steel man it, it is because running a for profit business also requires efficient use of limited resources and driving out waste from the processes

So "running government like a business" is a way to ensure tax money is being spent effectively and efficiently

to be clear I dont think that is the best way to accomplish that goal, thus why I disagree with it, but it is not "profit" that drives that statement

It came about because far far far far far too often government programs and spending are judged by their intentions, not their actual results.