HVDC (and even the grid in general) doesn't transmit all that much power. The largest currently existing line - Changji-Guquan UHVDC link in China - transmits 12GW. It's significantly more than what an average long-range link of current grids transmits, yes. But is it a lot?

Looking from consumption side, my home city of ~1 million people has several coal-fired plants, producing 1.5 GW of electricity and about 5GW of heating. Plus an hydropower station producing 6 GW. Most of that is consumed by an aluminium plant, but nonetheless, it's also part of the city. So that's roughly 12GW on a cold winter day (I suppose we do want to make heating cleaner as well), and probably 6 GW in summer. Heat pumps could be used to reduce power consumed by heating, but even the air-source pumps are not cheap, and they don't provide much efficiency gain in the cold. Ground-source pumps are extremely expensive and reqiure heat replenishment or the ground will freeze - such is the balance here.

So, the world's largest link to power just one city, out of tens of them. It quickly gets prohibitively expensive.

The only realictic answer, it seems, is annual-scale storage. I hope that "dirt pile storage" works well enough and succeeds, batteries are just too expensive and material hungry, hydrogen is problematic to store well either and we don't seem to have good enough scalable direct carbon capture to synthesize methane or propane.