Substations and generators usually have a continuous and peak rating. For example, a site I maintain has a substation which clearly states something like 630amp continuous, 800amp for x hours.Indeed (and I think a bit higher when there is electric heating) - and, when one thinks about it, that's not unreasonable as an average over time - 'large' loads (say, >1kW) are usually present for only a small proportion of the 24 hours of a day. However, I presume that there are times of day/year (like the infamous Christmas day morning!) when the average across properties might well get quite a bit higher than that.
Kind Regards, John