In a well insulated property, the greater efficiency from operating at low output temperatures outweighs the additional heat loss from no / a low overnight set-back. In a poorly insulated property, the optimum set-back is higher and the efficiency at that optimum point is also much lower because the heat pump has to operate at higher temperature in order to ramp up the temperature.
I don't know if they are available in North America, but in the UK we have hybrid systems available that use heat pumps for 80% of the annual heat load and gas for peaking / ramping. OpenTherm gas boilers can be retrofitted to be controlled in this way so you only add the heat pump. An air source heat pump driving a hydronic / radiator system in this climate can serve 80% of the annual load with a unit sized at 55% of peak heat load. Different climates will have slightly different numbers but it shows the power of a hybrid system as you save a lot on HP capex and also maintain redundancy.
The advantage of this system is that the failure-mode of an incorrectly sized system is an efficiency penalty rather than not being warm enough, the same as an incorrectly commissioned or sized gas system. (Most gas systems are not optimally sized or configured and are delivering 5% to 10% less efficiency than they could).
I don't know if these systems are available in ducted air configuration for the US market though.
> When it's truly cold (like < 20F) the heat pump will run continuously and struggle to maintain temp.
Luckily, pretty much the entire Western and Eastern Coastal areas, it doesn't actually get that cold on a regular basis, except a few days in the winter. The US is actually in an incredibly advantageous geographical position for at least 60% of households to be on heatpumps, as opposed to, say, Finland/Canada/Russia etc.
For reference I've lived in NC and TN near the mountains where heat pumps are pretty standard. I imagine we don't get the ultra high efficiency cold weather heat pump units that would be used up north, but they also get much colder temps than us. Several of the houses I've lived in have been recent construction (2008 and 2018), so well insulated and reasonably new & efficient heat pumps. For the last 2 years I've been in a house with gas, and it's just so damned pleasant... I know on paper that heat pump is better, but I really don't want to give up that furnace.