The benefit of owning a home is almost always psychological, not financial. If you take the money you'd use for a down payment and mortgage and invest it instead (after paying rent) you end up in about the same place. But the psychological benefits can be huge. You have much greater control over the place you spend most of your time. You can change it to your liking. You don't have to worry about rent increases or ow…
Yes, this is broadly correct. The free market will (roughly) arbitrage out any differences between owning and renting. The hidden factor is that whatever money you have in house equity represents opportunity cost that it isn't in investments. If you have 400k in a house and the stock market returns 6% over inflation, then the opportunity cost is 2k per month in interest, which is comparable to what you'd pay in rent.…
If you own $400k of stocks, you can sell any increment of dollars you want over time. You can take profit, you can take money out to cover needs, etc.
With a house, sure you can "take out home equity" but its just a loan against your home you have to eventually sell to cover or pay back.
It's like having a $400k position in your companies stock that you can only sell all at once with a 10% round trip transaction fee.