If one takes 50% of the equity at the time of the dirvorce and inflate it according to appreciation of the house.... that is equal to 50% of the current value of the house.
While I understand your point, that isn't exactly correct.
Example:
At the time of the split, the house was worth 150k, and had a 100k mortgage balance.
20 years later, the house is worth 400k, and is paid off.
250k is appreciation since the time of the split. 50k was equity built up prior to the split (which probably was a combination of paying down the mortgage and appreciation) and the other 100k is paying down the mortgage.
Equity is comprised of mortgage paydown AND appreciation. So, if you are making an argument based on "return of investment" you can't logically include equity paydown in that if only one party is paying down the equity. Then it can get even more complex by adding in the interest component.
In fact, an argument can be made that the party leaving the home had a 25k investment. (1/2 of the equity in the home at the time of the split) and that the party keeping the home had a 125k investment (1/2 of the equity plus the remaining mortgage). That would give the party leaving a potential appreciation basis of 16.67%, making there share of the 400k at 67k 20 years later. It could even be less if the interest component is factored in.
Would that fly in court? Absolutely yes if they had an agreement/contract at the time they split. If not, it would be really, really iffy in a partition suit.