For an NPC, more fiddly than I'd bother with. If I want damage output to be at a specific level, you can just ... make it do more/less damage.
I'm also not sure what EK/Pal combo would result in, characterization wise. It isn't super evocative?
Optimization wise, if I was min maxing, I would probably shave 1 level off EK and 2 off Paladin and put them into sorcerer or bard or something. Gives me 9th level spellcasting and the ability to launder slots through sorcery points, at the cost of 2 ASIs and a Paladin subclass feature. And if a Bard, whispers gives me (cha bonus) uses of +2d6 smites.
You spent a LOT of levels getting that 3rd attack; Fighter 2 gave you action surge, Fighter 3 gave you EK, Fighter 4-10 gave you 1 subclass feature and some ASIs. Often there is a better way.
EK 11/Paladin 2/Whispers 7 gives you almost as many HP, and much more powerful smites, and just as many attacks. (11th level spellcaster's slots, plus cha bonus 3d6 smite boosters from Whispers)
Taking two martial classes over level 5 is expensive, because the Extra Attack(1) dead level and how much potential it represents, wasted.