Technically Vader only "helped the Empire hunt down and destroy the Jedi knights." So technically he wouldn't have to be the main person, but I'm pretty sure still Darth Vader is supposed to be the main one killing the Jedi at least if we follow how the current PT continuity works into the OT trilogy. Becuase it could be that Vader wasn't always at the the second to the top of the Empire, which the line somewhat seems like it implies he wasn't always second in command, IMO. BUT that would seem to not work, at least if we are following the Vader backstory given in the PT.

BUT, I most certainly agree that they should have Vader, not he the weird non-sith dude be the main person to hunt down the Jedi.