It should be worth noting that home ownership isn't a problem at all. For example, simply because you want to visit disneyland, once every month, but cannot afford it, it doesn't mean that all of a sudden it has become somebody else's problem. If you're not earning enough in a free market, it's completely your problem (either you're not skilled enough, or have wasted your time acquiring a worthless skill with no demand).
Another thing to note is that, not everyone necessarily wants to buy a home. Some people prefer paying rents their whole life, because it's cheaper and more flexible. In that case, the government is simply confiscating their wealth, which could have been spent on business investments and things that they actually like, which is crucial for efficient deployment of capital and correct valuation of companies, in accordance with market demand. The government should stop treating people as kids, trying to design their budgets. Not only is that a violation of their liberty, it's also bad for businesses operating in the country, as mentioned earlier, and has significant effect on employment, wage growth and further investments in the region.
Expanding on the previous paragraph, in a socialized scheme like this, it's certain that not everyone is getting enough value, because the numbers wouldn't add up. For those who are overpaying (including those who want to buy, but have to compromise on the quality, locality, size etc.), it's certainly frustrating for the reasons that I've mentioned in the previous paragraph. For those whom you assume are underpaying might still not be getting enough value, because of segregation, low social respect, corruption draining the money elsewhere and providing lower quality homes than expected etc. Even if it isn't present under the current government, there's no guarantee that it won't be present under the future government. Statistically speaking, these socialist systems do tend to get corrupt over time and drastically go down in quality and efficient deployment of capital.
Finally, to close it off, if you think anybody in their right mind would tolerate the government deciding who gets to buy, at what price and where, in other countries, you must be a devout marxist.