I'm simply using your 20 year S&P investment example. I disagree it would be $170K.
20 year BWV stay would cost app $0, BWI 20 year stay (instead putting 10K in S&P) would cost $53,000 ($84K-$31K).
Not only that, but I can now put $3,200 each year into the S&P for the next 20 years ($64,000) that you can't. $4,200 for the room each year cash, or $1,000 each year in dues.
The last reported 20 year period on $10K put into the SP was 1996 to 2016, you would have $31,000.
$10,000 into BWV (about 200 points or 2 weeks a year in a studio) at the time would now be worth close to the same ($30K) in resale value.
The only real difference is the BWV owner would have dumped in about another $20,000 in dues. $30K total.
The closest apples to apples would be staying at BWI for 20 years for 2 weeks at app $300 a night or $84,000.
The $31,000 comes right off the $84K, so that only cost $53,000 to stay on cash.
But the BWV owner can sell and recover all of the purchase and dues paid, and if they wanted-dumped the $3,200 savings each year into the S&P on top of it.