Straight paladin has lay on hands, aura, different smites, and channel divinity.
Also have more spell slots and a feat.
No it doesn't. A Paladin 2/Bard 10 does not have Aura or Channel Divinity and that is the mix needed for a 6th level smite to do once a day what the 12th level Paladin/Rogue can do twice a day.
Add more Paladin levels to get that stuff and the Rogue multiclass is outrunning you even with your maximum smite being used.
The Rogue multiclass DOES have Lay on Hands and DOES have a 2nd Paladin spell.
You do have more spell slots but every time the Rogue makes a sneak attack it is the equivalent of your guy burning a 3rd level slot on a smite. This means if you want to match the Rogue in melee damage you have LESS slots to actually use on other spells. If you ignore multiclass minimums, you also generally have a worse chance of landing those and getting the enemy to fail the DC. If you use the multiclass minimums that is a huge nerf to the Rogue and he is not much of a spell caster because his DC is so low.
If you use the multiclass minimums then a lot of your points here regarding spell slots become legit in play. He can't use the slots effectively for much other than divine smite. As a matter of fact if you put the multiclass minimums in place, and want to optimize this build, this Arcane Trickster/Paladin goes from max Intelligence (with no minimums) to dumping Intelligence and maxing Charisma. He gets GFB and Truestrike through a feat on Charisma instead of for free as a Rogue on Intelligence and the only combat spells he can cast effectively are Divine Smite and the one other Paladin spell he can prepare. That is the whole point! What you are saying here regarding spells is true in play ONLY when you keep the multiclass minimums in place.
Also, your can't use Cunning Action when you smite.
I know, not when you smite, but he can do around 40 damage at will without smiting and your Paladin/Bard can't.
Depends on the number of battles you have in a day. A lot of little battles really favors the Assassin. Both from the bonus damage and the Initiative boost giving them more turns.
Not really. The damage you show above assumes the Assasin wins initiative.
With advantage and a +5 there will be a lot of times you don't win initiative at 12th level with the 2024 monsters. Something like an adult Black Dragon is coming in with a 22 Initiative. Advantage and +5 vs 22 loses that most of the time.
Now you can get alert .... which is a second Origin Feat to do slightly less damage than the guy who took no origin feats at all. But even with a +9 and advantage you are still going to lose initiative often at 12th level.
