You have to include the imputed value of rent in the calculation because you are getting value by living there.

Yes, but you are not making a large capital investment when you rent...

The best way to think of a house purchase is as two wholly separate things: first, you are starting a little business as a landlord. Capital has to be found, maintenance and taxes have to be paid, and in return you get some rental income from somebody. This is an investment. One which is pretty attractive in the US relative to elsewhere because of the weird mortgage market and the tax advantages on interest. US houses historically rise in price on average over time, around inflation + 1%/year if maintained but without improvements, so with easily available financing and leverage this can sometimes be attractive even when the rental income isn't. You go into this business only if you have the financial capacity, you think the financial returns will be worth it, and that they will be better than any other uses you may have for that capital.

Secondarily and separately, you are signing a lease on the same property and paying rent on it to that landlord (by coincidence you), in return for the use of it. The rent is at fair market value and might be more or less than what it's costing the landlord. The lease is slightly unusual in that you get to pick the place, it can't be cancelled without your permission and you are able to talk the landlord into approving any changes you want, but it's mainly just payment in return for use.

This isn't a novel view. Inflation is calculated based on imputed rent rather than mortgage payments for exactly this reason: only the second transaction is a useful measure of that person's expense profile. The first one (the equity portion of it) is useful for estimating the person's net asset value and investments, but the landlord's profitability on the deal isn't a useful input to inflation.

The decision on whether to buy or rent is pretty much only a factor in the thinking of the "landlord" half of the equation--is it a viable and attractive investment? For the tenant, it's only the small unusual non-financial aspects of the lease that make any difference--it's otherwise a wash whether your landlord is you or someone else.

Jim