What I don't get is, why is it important for melee rogues to be good, and especially as good as Barbarians or Paladins? A Barbarian while raging effectively has 3x the HP of a Rogue vs most melee combatants. They have a fraction of the skills and none of the mastery, they lack evasion which combined with how their rage works means they'll never be as good of scouts, melee combat is all they're good at, and they're very good at it. So why would Rogues need to be as good or better at it than they are?
FWIW they absolutely would keep pace in damage; they have access to all the same options as a Barb as far as damage increase, and a Str based Rogue has terrible AC and survivability without a dip but damage wise has no real downsides. They also have the same number of attacks, *everything* in this game is "possibly-will-be-nerfed" and bonus action attacks are currently just as good as regular action attacks outside of Haste. But it's a terrible choice because you take a far less survivable class which excels on picking its positioning and taking out priority targets and force them to be in specific spots, at melee distance to their foes, without any advantage to that choice whatsoever.
Melee just isn't a thing Rogues really do or are good at, it's a thing they get away from very easily, and if they're stuck there they can do ok damage, but it's not where they shine at all. Much like Barbarians don't shine as scouts. Can you make it work, and can they do it in a pinch? Sure. But they'll never be as good at it as a Rogue, nor do they need to be.