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I have two heat pumps at my houses and 15 at my office building. None of them have aux heat. They all work fine through the winter (in the mountains with lots of snow)
There's your problem. Should be ~10F or lower. Any decent heat pump still has a COP of >2 at 10F. So on cold nights you're easily using >2x more energy than you should when you're running aux heat.
My heat pump is >10 years old and I run it when it's 5F outside. It's not happy but the COP is still >1.