It looks like I'm just mistaken on this one, it seems that in some markets rent is cheaper.
I think you're right that it's not apples-to-apples though, I suspect that median rental stock is typically less well maintained than it would be if it were owned, in the markets where rent is cheaper. I think most people are indexing their price point on things like square footage, yard, location, etc., and not necessarily all of the factors that contribute to the cost of ownership to the landlord.
> Consider that for any given house, rent must cover the owner's mortgage, so it cannot be less than the purchase costs.
While this is true for owners that buy with a mortgage and then rent the property, I don't think this logic works in general -- it's not uncommon for the owner to own the property outright; this could be an individual that inherited a house or paid off their mortgage, or a large company where they are investing capital in houses instead of borrowing (e.g. a REIT); in that case you have a target yield to clear, but no "mortgage costs" per se.
> I'm not sure I have the energy to stay on top of it every month.
The standard recommendation here is to put your money in an index tracker, which has very low fees and essentially replicates the performance of the S&P 500 or whatever market you want to track. https://investor.vanguard.com/etf/profile/performance/voo would be one.
Anyone who bought the S&P and held it for 10 years made about 14% YoY (more like 10% if you take the last 30 years), and that's not considering the liquidity premium (i.e. you can exit your stock position whenever you need to, whereas selling a house takes time and effort).