Paladin 6 is very good, especially if your Cha primary.
That said. I would do bard over sorcerer.
Sure, though sinking 6 levels into an MC is a big ask in 5e. Whether you do it as Hexblade 1/Paladin 6/Hexblade +N or Paladin 6/Hexblade N or whatever else, it's a lot.
Two invocations at level 5 gets you most of what Paladin offers. The +Cha to saves IS really nice, no question, but "+Cha to saves, Extra Attack, and slightly inferior Smite ability" may not be worth 6 levels and saving the two invocations you would've spent on Eldritch Smite and Thirsting Blade. Hexblade alone gets you medium armor and shields, and medium armor is actually semi-viable since you don't need
to focus on Dex for attack and damage. The Paladin spell list isn't half bad, and being able to cast some of those things with Warlock slots is
nice, but even piling all that together I'm not sure it's "6 levels of MC" nice.
Why Bard over Sorcerer though? Being able to burn spell slots for SP or vice-versa is the big draw of the Sorcerer/Warlock. Bard is a wonderful all-rounder (something I've thought about quite a bit with speculative builds), but I'm not seeing what the benefit here is compared to Sorcerer. Especially if you go Divine Soul (which you probably should, unless some other consideration comes into play.)