My home appreciated in value a great deal. Does this make any difference if I don't want to move?

Depending on your State’s property tax regulations, you may have the pleasure of paying rising taxes on your house. I live in WA state. We pay close to 1% based on the current market value. Really nice that I bought a 1920’s house with a tax value of $1000, tore it down, built a nice new home when the property market was dead, and now pay more and more through the nose every year.

If you’re paying for PMI you might be able to have the house reappraised and then cut out that expense.

Are you sure that your property has actually appreciated? That is, when you bought it three years ago and paid 121,000 (assumed to be market value). Is the 250,000 you say it is now worth the market value, or just the appraised value (for tax purposes)? Quite often, municipalities will overvalue properties to raise tax revenue without “raising taxes”.

You are providing the correct facts AFAIK. However if you take out an RM and the RM balance ends up >= the house value, from your heirs POV it is pretty much the same as if you’d given the house to the lender rather than them. Not the same in legal form, but in substance. As compared to a situation where you didn’t do any borrowing but just tried to make it on Social Security, pension and savings if any, etc and the house ended up the free and clear possession of the heirs. Which is the comparison a lot of people make I think, though maybe it’s not a reasonable comparison.

Another aspect of RM type product which can be a positive is if people get a RM line of credit even without necessarily drawing on it, but as emergency source of money. The benefit there is the amount of the line steps up over time by a formula. So, even if the market value of the house turns around and goes down, you can still borrow that stepped up amount, with the govt gtee covering the lender’s exposure to lending more than the house is now worth. If you waited to get a home equity line till after you needed the money and say the housing market has also tanked in the meantime, you could borrow less. A RM line of credit can serve to effectively lock in the appreciated value of a house without selling it.

On property taxes and home values, where we live there’s no direct connection between the two. Rising property values tend to lower the political resistance to property tax increases and vice versa, but it’s not by a formula. We pay a rate on assessed values which don’t get updated for years at a time (it was 30 yrs before the most recent reassessment so the rate was greatly lowered after the reassessment or else taxes would have gone up by 4-5 times). Politicians have to explicitly vote to raise that rate between assessments: they don’t get an automatic revenue boost from a rise in market values. But this is in NJ with sky high property taxes, so it’s not as if this mechanism necessarily results in low property taxes.

This. My house has quadrupled in value over the past 20 years. We are not going to do anything.
What goes up also goes down. If you sit on your equity, you won’t have to worry if Zillow tells you that your house is worth less. If you take a lot of money out of it, and it is underwater, you do. Don’t let the equity burn a hole in your pocket - think in terms of cash flow.
The OP should read about what happened to people in 2008. To quote Dylan “I’ve been through this movie before.”