Forget the ER part of the equation - it doesn't make sense to purchase a house unless you plan to be in it long haul. (Greater than 7-10 years). The transaction costs (transfer taxes, broker fees, escrow fees, points, etc.) all add up... and tend to be sunk costs unless you amortize them over a long enough period.
As far as rent/own in ER... That's determined by the housing market, personal comfort level with having an illiquid asset locking you to a location, etc.
I currently "own" my third home, and consider it a part of my FIRE plan in that we were able to "time the market" and buy at a relatively low cost when value has risen even over the paltry two years that we've owned it. We now have quite a bit of equity in the home due to paying down loans and increased value estimates, and the value is projected to continue rising at about 6%/year over the course of the next several years. So, you CAN own homes for shorter periods, and you CAN use it as part of a FIRE plan, but there is also a lot of risk over the short term:
- My first property, purchased with zero down payment, gained 50% in two years, and I took $60,000 in profit, which I then directly applied to...
- My second property, which LOST roughly 12% over two years, costing me $30,000.
So, over the four years of ownership, I "made" $30,000 in the simple terms (this does not include taxes, interest, etc., but also doesn't account for the income tax benefits...) bottom line, I still "made money" over four years with 0 money down thanks to my VA benefit.
Note: this is not a SMART plan at all. I got out before the bubble truly burst, which is why I was able to walk away with anything resembling a profit.
THAT said, I disagree somewhat with your first point that the reason not to do it is to avoid all the fees associated with home purchases because there are ways to minimize and almost avoid them altogether. If you're able to go in strong with a good down payment and pre-approved mortgage (or just cash, ideally), you can often negotiate the seller to pay a lot of the closing costs. We paid less than $500 in total fees on our most recent home purchase. Escrow balances and HOA "account values" are refunded upon resale, so there's not as much loss there as it might appear (excepting, of course, the opportunity cost of investing those monies elsewhere for however long you own the home). if you can find a seller willing to pick up those costs. One way to do that is to find a "corporate" seller who is just looking to lock in their profit, and can often choke down a small percentage of their profits in fronting your closing costs just so they can sell and free up the money.
Complicated math involved, but overall I agree that short-term home purchasing is absolutely not a good way to fund ER, and based on my experiences both positive and negative, I would put a 5-year minimum on home ownership (market-dependent). If you CAN sell in a seller's market (and then rent, move to another market, or find a good deal), that's the way to go, but that is sometimes much easier said than done.