I agree with your general analysis, but I'm also seeing that it's becoming harder and harder for the average joe to get into the real estate market. Unless you can make a hefty down-payment banks just won't talk to you. The big driver of inequality going forwards is going to be between those who managed to get on the property ladder and those who didn't.
Of course if you have an investment portfolio adding an RETI is probably a good idea, but it's not really comparable to investing in actual real estate.
I have also invested in vehicles (private offerings) that fund residential construction especially in housing constrained markets. Very nice reliable returns
Obviously if you're already rich then you have lots of better options to become even richer (like the ones you've mentioned), but they're not really open to your "average joe", if for no other reason than that most of them require you to be an accredited investor or require a high minimum investment.
This ignores the rates-price and inflation-rates nexuses. When inflation goes up, ceteris paribus, rates rise. When rates rise, all else held equal, the price of leveraged assets like real estate falls.
TL; DR this trade is an arbitrage only if you've perfectly hedged the price of your underlying asset, the house.