As I'll explain, and as you won't be surprised to hear, government value is far tinier than you may think. Perhaps the main reason that people think governments provide so much value is because they do not think of alternative providers or the countless ways that the public sector could be improved. That's not to deny that the government is worth having - it's just a very mixed bag.
This principle is easily explained – when you go out tonight and spend £100 in your local supermarket you put up the price of everything else by a net total of £100. If instead you burned the £100 (and of course I wouldn’t advise it) you would decrease the price of everything else by a net total of £100. Naturally those sums are so small that society never notices when we’ve made the economy richer or smaller, but technically we have.
Imagine this as a microcosmic example of a macroscopic state of affairs; the government hikes up my taxes by 13%, which means I have 13% less of my equity to spend. The government gains more roadworkers or local council administrative officers, but my gymnasium loses in the subscription fee from which I withdraw. Then the gymnasium has less money in its bank, which means that bank has less to loan to Sue for starting up her new business, which means Sue’s shelf prices are higher than she planned, which means Mary her customer spends more on a washing machine, which means the curry she was going to have at the weekend is forgone, which means Roshes the Indian restaurateur has less money in his till, and so on.
That is how the economy works – and no government can make us richer on average, they can only shuffle money around from one place to another. There is also the little matter of the futility of governments getting involved in prices. To emphasise this point, you have to realise that prices find their level based on the entirety of human market transactions in the global society. It is literally impossible to make this more efficient by tweaking a few knobs - impossible.
To illustrate this, suppose the government decided to take control of the fruit and veg industry, whereby everything grown, imported and exported is under their management. Everyone in society would still be best off if all fruit and vegetables continued to be priced at its market clearing rate, because any price the government set outside of the market value would either be too high or too low, which means there'll be the wrong amount of fruit and vegetables.
I'd like to draw your attention to this
article from American economist Robert Murphy, who roughly (but soundly) calculates
a $2.6 trillion increase in annual economic output if "the government were to
restrict itself primarily to its classic role of protecting the country's
residents from criminals and invaders".