Then, couldn't you argue that if individuals are responsible enough to choose things for themselves, they should also be responsible enough to choose a good government? If so, arguments against intervention then become irrelevant, because it's really our own intervention.
If 51% of people vote for the other 49% to be raped by government soldiers, are you going to say that they brought it upon themselves, and it's their "own intervention"?
Secondly, you ignore the reality that you can't vote for single proposals. You must vote for a package, a bundle of policies. People can't pick and choose the policies they like from Liberal, Labour, Greens, like they can pick and choose products from different supermarkets.
Even then, the political process imposes uniformity. The laws must apply to all. So if 51% vote for blue ties, and the other 49% votes for green ties, then the other 49% loses out, everyone must wear a blue tie. In a free society, you wear whatever color tie you want. You have freedom of choice.
What you call "our intervention" is the government's suppression of other people's choices by superimposing on them a collective plan, created by third parties, armed with the power of government and exempted from paying the costs that these collective plans impose on others.
It's one thing to argue that government coercion is sometimes necessary but it's another thing to try to dress it up as if it's not coercion. The sort of government intervention you are talking about that suppresses individual choice and freedom makes the assumption that people are too stupid to make their own choices.
If a man chooses to gamble, by what right do we prevent him from doing so? We may argue with him, seek to persuade him that he is wrong, but are we entitled to use government coercion to force against him? In a society based on free discussion, the appropriate recourse is for you to seek to persuade him that his tastes are bad and that he should change his views and his behaviour - not to use coercive power to enforce your tastes and your attitudes on others.
In the end, is there not always the possibility that he is right and we are wrong? Humility is the distinguishing virtue of the believer in freedom; arrogance, of the paternalist.