However, if a DC detects that the _grid_ is wobbly (voltage or frequency deviations) the DC will disconnect without warning, and switch to its batteries and generators.
The grid complains because it's suddenly lost hundreds of MW of load. For the DC to have isolation capability, it would need a load-sink which can consume roughly the same power as the DC in normal operation, and can take in that load at a moment's notice.
It's a hard problem to solve, and probably better managed at grid-level than DC-level.