Heating (and AC) are not problems solved by pouring more energy in your home but with insulation.A passive house is a reality even for cold climate, and they don't need storage for cooling/heating. Then you are left with your appliance that have to run outside of production time, but this is rather small.
Insulation alone doesn't necessarily solve for AC / cooling. Modern houses with more insulation than ever are some of the most prone to overheating. So much so that the UK's latest update to building regulations, Part O, are specifically targeted at overheating.
Insulation slows the transfer of heat so in theory it should help on hot days as well as cold. The problem is modern houses lack thermal mass to smooth out temperature changes. They're quick to heat up whether wanted or not.
So, you have solar gain heating up rooms on a sunny day, better insulation reducing heat transfer, and high levels of airtightness trapping the indoor air.
Building design has to adapt for a changing climate.
Many existing homes will need air conditioning to maintain a comfortable environment regardless of how well you insulate them.
