That's kind of the catch, isn't it? All the government agencies that do their job with efficacy wouldn't be the ones you'd be made aware of. Only when something goes wrong do you become aware that your local water board performs useful work.
To the point though, regulation ensures our planes crash at a rate of less than one per 21,000 years of flight time. Food safety regulations have dropped e.coli poisoning by half in 15 years. I believe there's a state by state comparison on road deaths following seatbelt regulations, showing a clear causative effect.
Maybe we'd be a bit more aware of the fact that the government actually works pretty well most of the time if we sent our little prayers of gratitude to the Federal Aviation Administration on touch down instead.
Despite this, my larger point is that it works even better in most other Western countries. You can see this quite clearly in at least one case by comparing public expenditures on healthcare per person. Single payer health insurance is more effective per dollar, regardless of possible criticism on other grounds.
2.
Largely, because the free market is a poor regulator, and the government does it pretty well most of the time. To break it down:
a) there are things we'd rather corporations didn't do, for the good of society as a whole - such as misleading consumers about ingredients, or hey, hiring local cartels to break down some unions in Columbia.
b) consumer action by itself is ineffective. Boycotts, in the vast majority of cases, are too transient to be effective. This is compounded by the sheer number of companies one must try to keep track of to be an ethical consumer, the cartel example above is Coca-Cola, for example. Furthermore, say a mining or oil company is doing massive ecological damage. It's just too difficult to be able to track the produce of that mine to any decisions you make personally to effect what minute sway that decision would have.
c) the solution is to codify our standards for this behavior by social agreement, and penalize corporations that are found wanting. This is a regulatory body that provides a net benefit to society.
I do agree that the government has protectionist and overreaching regulations in certain areas, but I believe it's remiss to label the entire government as such. "Big" and "small" government are rhetorical buzzwords that prevent people from evaluating regulations and regulatory bodies on the case by case basis they require.