It's probably true that you'd be financially equivalent, but some people don't prefer to move with little notice due to rental changes forced upon them.
I suppose if you account for this extra cost (which may be non-monetary, but one can always assign the inconvenience using a dollar figure...) then renting could be worse off.
Yeah, I don't even care if owning a house is financially worse than renting. It's mine! There's no landlord who decides to inspect it, or evict me. The cost of the mortgage is subject to a pre-determined process, and I can fix it to provide predictability. I can extend it, improve it, fix it or redecorate it. It represents power over my circumstances, and long term stability. How do you put monetary value on that?
it is possible to make a guess at the monetary value of these advantages, by comparing the difference between the cost of renting vs cost of owning (including cost of capital). Of course, the value of owning is different between different people (some might prefer renting due to the flexibility of moving at a moments' notice for example).
And in fact, if it turns out that owning is lower cost in total (even taking into account the cost of capital), then it would make a lot of sense to buy! And in some areas, this is definitely true.
I suppose if you account for this extra cost (which may be non-monetary, but one can always assign the inconvenience using a dollar figure...) then renting could be worse off.