But "heat pumps" (which is exactly like AC, but in the UK 3x more expensive because its "renewable") need to run for heating.
So I agree with you, solar and AC are perfect for cooling, heating might need other sources of electricity.
But I suspect heating is more expensive than cooling.
In Romania (45-46 degrees latitude) I can tolerate up to 25°C, and an uncooled room (that is not directly below the roof) only ever gets to 28°C, so it'd need 3Δ°C.
Whereas in winter, an unheated room can get to 14°C or lower, but the lowest temperature that doesn't affect me working from home is 23°C, so it would need upwards of 9Δ°C of heating.
Therefore, a heat pump for heating needs more power than an AC for cooling, which is why it would be more expensive.