A increasing percentage of new construction gets heat pumps. Some replacement HVAC units make the switch, but there is still a large portion of people who won't because of misinformation and/or stubbornness.

But, unfortunately, most existing residential systems do not use heat pumps, under 20% in the US I believe.

No.

Typical gas / coal plants are ~40% efficient. That means that if you do natural gas -> electricity -> heat pump, you only have 40% of the energy available to you. Yes, Heat-pumps then multiply that 40% energy out into "energy movement" rather than heating, but its a huge efficiency break.

If you instead run a pipe from the central source of natural gas and then burn the natural gas inside of a home, you have something like 95% efficiency (5% lost in the chimney).

Its only in the most recent decades have heat pumps actually become more efficient than burning natural gas inside of homes, because you have to factor the inefficiency of the power plant in your conversion. So today we're finally in a position where modern, advanced, efficient heat pumps are worthwhile. But go back just 20 years ago and the math still pointed towards burning fuel inside of our homes as the most efficient solution.

Nope. Burning gas and direct electric heat of some sort are still the most prevalent forms of heating in the US, and often have separate cooling systems.

New building almost all use heat pumps because they are a no brainer, but a house built 60yr before the technology existed may still be using a very old heat source. Many people do not have the 20k+ to retrofit their current home with heat pump technology even if it can save hundreds/month on their power/gas bill,so here we are.

On the plus side, it is one of the lowest hanging fruits to reduce your bills long term, along with sealing drafts, insulation and replacing your water heater, so many people who have the means are opting to do all of the above.