> the goal of business is to drive profit, not human welfare
I agree, and that is indeed a problem.
> The goal of the government is to drive human welfare, not profit.
I disagree strongly: the goal of government is power. No-one runs for office to make the world a better place: he runs for power or, if we're very, very lucky because he wants to be the one to make the world a better place.
To your dialectic of government & business, I'd like to add a third party: the people. We're not pure either, of course (as a group, we like to oppress, ignore & line our own pockets!), but we're the ones that create government; we're the ones it ought to serve; we're the ones who ought to hold it accountable.
Some of us fall into the trap that whatever a corporation wants is okay, others into thinking that the State is always right, others still into thinking that the People are always right. The truth is that all of them are sometimes wrong. There's no real solution.
But let's try to minimise the amount of violence in our society, and try to maximise the utility we get for that violence. Am I okay sending men with guns to wrest your property away in order to fund the national defense? Sure. Am I okay sending them to prevent people starving in the streets? Okay. Am I okay send them over in order to finance a cowboy poetry festival? Hell no.