Except, also as we know, some systems nowadays have a lock-out option that prevents the auxiliary/resistance from running (except during defrost cycles) until the ambient drops below a chosen (programmable) temp. Being as temps here rarely drop below 30°F, my lock-out is 25°F. At "extremes" approaching that, a 10°F recovery may take 4 hrs at =<30°F, but I find it perfectly comfortable being that the system is blowing warm air the entire time.
If a cold snap dropped us to 20°F, I'd probably drop the lock-out accordingly.
How well a system can handle the heating load sans resistance depends on several factors, including such things as wind / air leakage. If the house is not well insulated and weatherstripped, a very cold still day is perhaps not as much of a problem as a very cold WINDY day.
The required electric capacity for a heat pump is equivalent to a non-heat pump air conditioning system with standard resistance heat. There's nothing unusual about the resistance heat that's involved.
L, there are ground-source heat pumps (either water or earth) that are more efficient (for both cooling and heating) and better able to deal with ambient extremes.