High load in the day during sunlight is mostly true for summer heat, but in the winter you have cold evenings which requires base load or storage, combined with solar angle/efficiency being worse in the winter.
If the energy is for heating then there is always the option of storing the energy as heat. Which is much simpler than storing electricity.
Cooling takes more energy than warming, so the summer daytime use is higher. Summer = warm evenings. I'm from Indiana - it was almost always cooler at 10am than 7pm, even in the winter. It takes time to heat up or cool down. I'll also mention that nights and weekends use less power because business and industry tend to shut down during these times.
Which would somewhat logically mean that despite the efficiency being worse during winter, it isn't as much of a strain because power demands are less.
Are heat pumps common for factories and offices, which account for a lot of energy usage during the week?
Anywhere they aren't common, cooling generally is going to require more traditional methods and the energy cost is greater than just heating. If it were the other way around, poor folks would use a window air conditioner to heat. Cooling pretty much always creates warming - which is the reason it is vented outside.
The energy use I linked to doesn't actually consider where the energy comes from - just the use itself. These methods aren't going to use more or less energy depending on where the energy comes from. Heat pumps would make less usage due to efficiency.
Does that mean that it is untenable?