My guess is that on a financial basis, owning wins out in the long run. But you have to stay put long enough. If you move around every few years, you're going to spend a lot in closing costs/commissions, etc.
It cost me roughly $175,000 up front, to get into my current house. That included a 25% down payment, because I didn't have the income to get into it for 20%, or less, as well as the associated closing costs. I'm coming up on the 5 year anniversary in this place. So, just allocating the down payment/closing across 60 months, that's $2917 per month right there.
My mortgage was initially around $2900/mo, but I've refinanced since then, and it's now around $2530/mo. But, depending on how creative you want to get with the accounting, you could argue I've essentially been paying $5400+ per month for the house, not including utilities, maintenance, etc.
I have no idea what a place like this would rent for. Most likely, there aren't a lot of comps out there to get a gauge on a ~2500 square foot, 4 br/2.5 ba two story with an oversized in-ground pool on a sprawling, secluded 6.5 acre lot.
Still, I could see the argument being made for investing that $175,000, and then renting a more modest place, for whatever I could get for my $2500-2900/mo mortgage.
Over time though, the mortgage becomes less and less of an issue, simply because of inflation. For instance, that $2900 I was paying in 2018 would be like $3500 in 2023 dollars. While I'm only paying around $2500 now, if I hadn't refinanced, it would probably be around $3100-3200, as property taxes and insurance went up.
As for maintenance, the house has been pretty minimal so far. I've had to make a few minor toilet repairs. One light in the kitchen went bad (wiring problem), but there are plenty of other lights, so I just left it for now. In 2019, the refrigerator stopped working. That was about $300 to fix. And earlier this year, the outside unit of the downstairs HVAC went out. That was around $450, but included some maintenance I had as well.
I'm on well and septic, so no water bill. Every once in awhile, I do have to add chemicals. Solar salt that comes in 50 pound bags, and sodium hydroxide that comes in a gallon jug. I just bought 5 bags and 4 jugs, for about $97.00. But that expense comes around infrequently enough that I don't really keep track of it. Last time I had to add anything was sometime last year, I think.
Now the swimming pool has been a different story. One year I had to have the sand filter replaced. And then another year I had to have the pump replaced. I forget the exact cost, but I think each one was between $1-2K. I also had to rebuild the roof on the pump house, but I did that myself, and it was only $100-200 in material.
Anyway, with regards to renting vs buying, I made the right decision, for my needs/mindset. But, I am only a sample of one, and as the EPA disclaimer says, "Your Mileage May Vary".