At the point where the house is paid off it is an asset with two possible uses--you can sell it or you can live in it. (Actually, of course, there's also the possibility of renting it out, but that really amounts to doing business as a landlord and I'm not dealing with that here.)

If you sell your house, its value is whatever you can sell it for.

If you live in your house, its value is the amount by which it reduces your expenses versus what it would cost to rent instead. Now this is obviously a complex calculation--every place is different and each person has to make their own adjustments, whether for the "equivalent" rental or the place they actually do rent.

But let's put aside for a minute the "quality of life" aspects of home ownership versus renting. (Not because they're not important, but because they're not really economic. Let's do the economic part of the analysis first, and then do the quality of life analysis after.)

My fundamental point is that the economic result is the same, whether you own a "house" or whether you own some hypothetical investment with a return equal to the cost savings of owning versus renting. If the cost difference is large, then the equivalent investment is large. If the cost difference grows, then the equivalent investment needs to grow too.

(As an aside--rent will generally go up, but so generally will property taxes, insurance costs, and home maintenance. Only time will tell which will go up faster, but I think simply assuming that they'll go up about the same is a reasonable first guess.)

So I think my analysis does cover the "home appreciation" part of the question. Just as you might be able to sell your house at a profit, you might also be able to see the hypothetical investment at a profit.

If you do this analysis for your house, you may well find that the hypothetical investment has a value that is much lower than the value of the actual house. If the house a nicer place to live than the rental that you're using for comparison, then that explains part of the difference. (Do the analysis with a larger apartment or a rental house, rather than a small apartment, and you'll see that the hypothetical investment becomes more valuable.)

You may well find, though, that the economic value of your house plus the adjustment that you want to make for the higher standard of living that comes from living in a house, doesn't explain the whole difference in value between your house's market value and the value of the equivalent hypothetical investment. Feel free to make other adjustments (or simply to assign an arbitrarily high value to the benefits of living in that particular house), but let me gently suggest that the market value of such a house is not justified by its actual economic value.