> over the long term on average home prices don't increase.
I assume you mean adjusted for inflation here? Even then that hasn't been true.
The problem with renting is that you're still paying the mortgage, only in the renting case you're also paying the middleman who then pays the mortgage. This is why rent per month is higher than mortgage per month for the same house. So the returns from that downpayment you instead invested need to make up for the monthly loss in rent, plus the lack of an asset at the end of the process.
It's not a small difference either. My current mortgage is $1250/month for a single family home. 13 years ago when I was renting the rates started at $1600/month for a tiny studio apartment unless you were willing to commute an hour each way. Rents have gone up in the meantime. You need to be making some baller returns on your downpayment if you're going to beat that.
This comparison isn't entirely fair because the rental unit also included maintenance and groundskeeping. In my house I have to do all that work myself or hire someone. However, in the rental unit I had to pay for the utilities. This is a problem because the landlord will never replace something like an AC unit or a refrigerator with anything but the absolute cheapest and most expensive to run model. In my house when I replace it I have the option of buying the high efficiency model and enjoying the cost savings over the life of the unit. Plus when something breaks in my home I just fix it or go out immediately and hire someone to fix it. In the apartment you have to contact the landlord who then sits on it for two weeks before contacting his maintenance guy who only comes by once every couple of weeks to look at it and then order the part so maybe he can fix it on his next visit. In the meantime I'm freezing my ass off with no heat for all of January. I don't miss renting at all.