The mistake you made was using the future value of the saved money to pay for the present value of a home. Home prices in the Bay have also historically appreciated about as quickly as the stock market, but even if we assume they appreciate at 5% and you could get an 8% return investing money, you get taxed on the extra returns of your investment in the range of 30% after LTCG and state taxes, so your post-tax return discounted by the house price appreciation is basically 0.

A lot of words to say that your calculations are wrong and even if you take on a relatively high amount of risk+reward by investing in the S&P 500 you probably still won't save enough for a house in a region with good schools in 30 years. Which I think if you're making two hundred fifty thousand dollars a year, is pretty unreasonable.