Your math may well be correct but I can't follow it without a spreadsheet, so let's do a simpler example with two different appreciation scenarios.
Scenario A: I buy a $100k house with $50k down and a $50k mortgage. House prices don't change. I sell the house, then buy another $100k house. I'm still at $50k in equity and I still owe the bank $50k.
Scenario B: same as scenario A, but this time, all home prices double, including mine. I sell for $200k and now have $150k, which I use to buy another $200k house. I now have $150k equity, but I still owe the bank $50k.
In Scenario B I'm better off than someone who didn't buy the house before prices went up -- a fact that should surprise no one -- but I'm not necessarily better off than I would have been if prices hadn't doubled at all. I still owe the bank $50k in both scenarios. The housing price appreciation hasn't actually helped my finances unless I sell the house or use it as collateral for loans, neither of which I am interested in doing. Because I own the house to live in it, not to use it for financial engineering or speculation.
Scenario A: I buy a $100k house with $50k down and a $50k mortgage. House prices don't change. I sell the house, then buy another $100k house. I'm still at $50k in equity and I still owe the bank $50k.
Scenario B: same as scenario A, but this time, all home prices double, including mine. I sell for $200k and now have $150k, which I use to buy another $200k house. I now have $150k equity, but I still owe the bank $50k.
In Scenario B I'm better off than someone who didn't buy the house before prices went up -- a fact that should surprise no one -- but I'm not necessarily better off than I would have been if prices hadn't doubled at all. I still owe the bank $50k in both scenarios. The housing price appreciation hasn't actually helped my finances unless I sell the house or use it as collateral for loans, neither of which I am interested in doing. Because I own the house to live in it, not to use it for financial engineering or speculation.