Peaking does not cause blackouts; peaking prevents blackouts. I'm thinking that perhaps you're confused about what a peaking plant is.
Yes, but cross country grid loading is a bad idea. Very bad.
Interconnected HVDC grids offer increases in grid stability, as cascading failures can't propagate through them (AC failures are prone to cascade as different parts of the grid go out of sync with each other). Yet most of the time a nationwide renewables-supporting HVDC grid is not used at near peak capacity (its capacity is sized for peak load transmission requirements, not average), and thus can generally have their power routed through other legs if one line goes down without curtailments (often, even, without need for peaking - it depends on timing). The grid itself is designed, as with everything else concerning electricity generation and transmission, to provide a statistically-guaranteed level of power reliability.
It's important to remember also that in the US you have basically three separate power grids today - west, east (which is kind of a patchwork), and "ERCOT", which is basically Texas doing its own little weird thing. To allow them to support each other, they have a number of converters, mainly DC ties. Basically, HVDC terminals without any actual long-distance transmission lines. So it's already done to improve grid reliability and economics. Also, certain parts of the grid already rely on long HVDC lines. Not just for "moving peak power because of intermittent shortages in one region", as a grid for supporting high renewable penetration does, but actual baseload. For example, in the northeast, RMCC moves 2 GW of remote Quebec hydropower to New England. It's almost always run at near capacity.
Europe and China uses HVDC a lot more than the US. Europe mainly for undersea lines, China to move power from inland to its densely populated coast. Both have major plans for expansion.