Heat pumps only really work well when they have access to fairly warm temperatures. They are kind of worthless in the far north and direct fuel use is significantly more efficient.

If you burn coal for power at 40% efficiency and run a heat pump at 400% efficiency that's only 1.6x heat gain ignoring transportation losses. Drop that heat pump down to 150% efficiency and heating oil can become a better option.

In most areas using solar thermal heaters with backup resistance heating is actually the best overall option. But, in most of Alaska heating oil is much more viable.