Here (Italy) the "base" contract for electricity is 3 Kw, if you install a heat pump you need a 4.5 Kw one, very often a 6 kW one.
The good news may be that heat pumps used for heating homes largely have peak hours in the late afternoon/evening/night and this can help leveling the production (traditionally office/industries/workshop need energy during the day and at evening/night there is over-production).
Still when you start adding up KW's, the size of cables, transformers/transforming stations comes into play.
Imagine a street block in a city, not too large, let's say 10 buildings with 24 flats each, they now need 240x3=720 KW, the current transforming station serving the block is likely around 400-450 KW, i.e. 20% more than half the theoretical needed power (how this is calculated is complex, it involves an estimated simultaneity factor and a utilization factor, this is only a rough approximation).
Now, suddenly you need double that amount, 6x240=1440 KW, even if you lower the mentioned factor, it is unlikely that you can get away with anything smaller than 650-750 KW.
And of course the cables need to be upgraded as well.
And recharging electric cars hasn't been taken into consideration, but likely soon it will be another common addition.