"Cold" basements rarely fall below 50 degrees Fahrenheit/10C. There's plenty of thermal headroom below that for heat pumps to work. Heat pumps already work outdoors at below freezing. I don't think there's anything to worry about.

More of a problem is when your water heater is within your conditioned space envelope and in the cold months when you are heating your space the hot water heater takes that heat. Its not a huge issue but you do run the heater extra for the heat that's going into your hot water. If you've got an air source heat pump outside then its just an extra step.

I was thinking the same thing. You don't get something for nothing. Assuming the water heater is in the conditioned space, it will just make the central heater work harder (and consume more fuel) during the winter months. Maybe this is offset during summer months when it can help the AC cool the space.

None of this applies if the water heater is not in a conditioned space, but that's not feasible in (common) environments with cold winters.

Heat pump models usually have a resistive element for use when the heat pump can't keep up, or when the climate doesn't cooperate. Then you benefit from the efficiency whenever possible. (Here in coastal CA I have mine set to only ever use the heat pump since the climate is so mild.)

The up-front cost of a heat pump is definitely an issue. IMO we should be doing instant rebates to even out the cost between the two so that it's an easy decision.

There are split system heat pump hot water heaters which allows you to exchange heat with the outside environment, eg. https://reclaimenergy.com.au/products/residential/

The all-in-one units can also be installed with ducting.