Varunastra does work with Nightblade support. If you have Nightblade supporting a skill, and wield Varunastra, you can use that skill and get the benefits from the support.
Nightblade support does not support skills if the weapon restrictions of that skill have no overlap with the additional weapon restrictions imposed by Nightblade. This interaction has nothing directly to do with Varunastra, nor can it - gem supportability is fundamentally determined only by the gems, external aspects of the character can't change supportability.
Originally, the support that add weapon restrictions didn't have that supportability restriction - you could happily support Ground Slam with Nightblade, or Cobra Lash with Close Combat. This resulted in a skill which was limited to be unusable, except with weapon types that couldn't use the skill. Varunsatra, by counting as all weapon types, was the only way to satisfy the conflicting weapon restrictions. But mostly what actually happened is players applied those supports because they could work with their skills, and then complained angrily that they couldn't use the skills because they no longer met the weapon restrictions.
The potential new extra use of Varunastra was judged less important than the large amount of player confusion and upset from expecting the supports wouldn't apply if there wasn't a way to use the resulting skill (other than having to have one specific unique). So the supports were changed to only support skills if at least one weapon type could use the modified skill. This additional supportability restriction is intentional.
This might change in the long term, but that would require other changes first to mitigate the problems caused by allowing those supports to apply to skills that, other than Varunastra, they can't do anything for. Far, far more players fail to understand that "Supported Skills can only be used with Claws or Daggers" is bad for their mace-weilding Glacial Hammer character than have a Varunastra in the first place.