Another big problem is NIMBYism and ideological opposition to air conditioners.

Installing a heat pump can require (city) permits, permission from your landlord (if renting) or HOA/condo association (if you own a flat in a shared building) which can either be or feel impossible to get.

Some cities have either actually or de facto (through requirements/regulations that are impossible or unaffordable to meet) banned air conditioners, resulting in people buying inefficient monoblock units that can't be used for heating.

Edit: Other regulatory hurdles come from rules about refrigerant handling. Refrigerant must only be handled by experts who are certified in proper handling and recovery (and who, of course, are now in high demand and charging princely prices for their work). This made a lot of sense in the times where 1 kg of refrigerant had 10 tons CO2e in global warming potential, ozone depletion potential or other dangers.

Nowadays, a skilled layperson can probably set up an air conditioner with quick-connect couplings by themselves, but they aren't legally allowed to. These cost something like 500 EUR, contain less than 1 kg of R32 with a GWP of 675, so let's say 500 kg CO2e of harm if it leaks. If you passed a law that landlords cannot prohibit installation, and any electrician that passes a quick online training can install them, you could have them all over the place very quickly.

These could then be used for covering some or all of the heating load in winter, but they'd also alleviate suffering in summer, and that's luxury, and we can't have that (especially as it uses energy to provide the "needless" luxury!)