The house price is set by what buyer's are willing to pay for them. This is taking into account that in median, 4 years of that person's work-output will be required to purchase a house.

In which country is that? Last time I checked, the common way for financing a house purchase in the entire Western world is through a mortgage loan, which makes the house price tied to the size of the loan a bank is willing to give to an average person.

That's not how prices are set. Just because I can borrow $X thousand dollars on my credit doesn't mean I go ahead and purchase all the big screen tvs and computers I want. Just because I can borrow $XX thousand to purchase a car doesn't mean I'm driving around in a new mercedes. Just because I can borrow $X million to purchase a house doesn't mean I will purchase real estate which will turn my net accrued savings to 0.

When people only think short-term (what's can I afford monthly) vs. long-term (what will I pay out over the life of the loan vs. what I'm getting now) they make mistakes. These mistakes are self-inflicted but these people tend to then blame any and all others for why they can't get ahead, why the system doesn't work, why the American dream is dead :).

That's besides the point. Most young people today can't afford a house. So they take a mortgage loan to buy one, and surprisingly, houses tend to be priced just at the level of the loan an average person can get.

The situation is different from the TVs and computers and cars because those are not considered as important as your own house. Most people eventually have to move out, so they have to participate in the game. I believe we call it "inelastic demand".