When rates fall, prices for assets like homes tend to rise in proportion shortly after, such that the cost to borrowers is approximately constant. The benefit of falling rates goes more to homeowners, even if they don't have mortgages.

And now their fully-owned houses are worth 1.5-2x compared to 2019.

Which is even better. They could take out equity release and spend what they borrowed.

But of course if you refinance to take equity out, now you're back to having a monthly mortage payment again. If you do it today, it will be a high interest mortage. If you're over 65 (as OP mentioned) you're probably soon retiring, so this would be a very bad financial move.

are reverse mortgage interest rates fixed or variable?

If they are fixed, anyone who refinanced in 2021 when rates were dead cheap and prices were sky high made out like bandits

A cash-out refinance (what people would most commonly do in this circumstance) is just a regular refinance, so terms could be anything a refinance can have. Usually fixed rate 30yr.

A reverse mortgage is a different thing, IMO always a bad deal but I guess could be ok in some cases.

Many people move multiple times in their lives. People also take out additional loans on their homes down the line to do remodels/renovations