People who have nothing to lose tend to make poor economic decisions and poor social decisions.
That's why home ownership matters. It's a poor investment vehicle only if you assume people would invest savings from renting into appreciating assets, rather than burn it on consumables. They won't.
So, yeah, government is involved because it's a collective action problem. Individuals and the market left to their own devices will reach a suboptimal equilibrium.
Is home ownership the _only_ answer? No. The problem is fundamentally cultural. But in the U.S. especially, subsidizing home ownership seems to be the most viable mechanism we can, as a society, agree upon. Probably because of our emphasis on individualism. In a society that highly values individualism, people will be more incentivized to strive toward home ownership than other alternatives. We went them (us) to delay other, less economically efficient forms of gratification.
In some Asian societies, for example, different cultural preferences make alternatives more viable. For example, they're more likely to emphasize investment in education. I'm pretty sure the phrase "book learning" isn't derogatory in most Asian societies, even for low-skilled laborers who feel disenfranchised and lack any intellectual ambition. (Not that those things are necessarily related--I strung them together for emphasis.)
In any event, the point is to keep people invested in the economy in such as way that their individual choices tend toward more productive activities. It's a channeling function.