IMHO, cheap gas has been the only thing propping the dollar up this past decade.
Best to take advantage of ridiculously cheap mortgage rates, hedge against inflation. I used to be the "pay it down faster, get some equity" mindset, but with rates this low, and factoring in the tax deduction, it's better to just pay the minimum and put the money elsewhere. Hell, even BOND is paying a better dividend than what I'd get by paying my house down.
I've already done that and have a loan at 2.75% since this past August. I'm hedged against asset inflation there, but I don't expect anything too crazy with home prices: in fact I expect them to continue to underperform things like stocks, crypto, etc.
The issue I see is that it's not necessarily assets like houses that will continue to inflate at crazy rates. It's the "everything else" that everyone can still afford day-to-day. That can be stretched quite a bit because people can cut back: stop buying high quality food or organic, reduce your data plan, stop wasting electricity and water, have only one streaming service, etc. And that's why I feel like my FI/FIRE numbers keep getting pushed back. I might even have to start practicing some of these things myself now and reduce expenses as much as possible.
Once that is stretched as much as possible you're basically at the 3 classes I mentioned: wealthy elites, upper middle class, and the "poor socialist" class. The government will provide UBI to that class to keep everyone happy... for a while. The wealthy elites will continue to fly their private jets, the upper middle class will live comfortable lives, and the "poor socialists" will no longer have to worry about making rent anymore. So things will be ok for a while (maybe a generation or two) until the 90% are tired of being stuck in their "poor socialist" tier, and that's where things will really unravel.
So what does that have to do with right now? You get ahead of all of this as much as possible and the only way to do that is to either 1) take a low rate mortgage as you mentioned and 2) buy stonks to and be on the upper-half of the K-shaped recovery.