I didn't say it out-damages the Paladin. Just said it's respectable if you take the right options. I do wonder how much damage it would have done if I'd played it as a Paladin and just crapped out Lightning Arrow and Hail of Thorns with all my slots. As it was, though, I relied more on Animate Objects than anything else.
A person can make them respectable enough in damage (that was my "mediocre" comment from earlier), but it doesn't get to the same levels and focus on damage is not focus on something else.
Recently had a PC in my campaign that went P2/Bd 6. College of Swords, so he attacks 3x per round and pretty much just uses his slots for smite. So he had 4/3/3/1 slots while the full Paladin had 4/3. MCing Bard with Warlock or Paladin is pretty popular.
The Paladin rescued Prince Thrommel and got a Sword of Answering as a reward, though.
MC paladin or warlock with sorcerers are popular too, for the same reasons. It's the features from those classes that a person is looking for and not the bard specifically.
The MC costs 2 levels and 1 spell progression level on the MC table. Those smites look good but they aren't sustainable and a person could just have used a couple of fireballs or whatnot instead.