Right, but EK doesn't get War Magic until 7th level.
Fair.
And you're assuming sword and board with War Caster, the weapon die is a bit bigger if we look at a 2H weapon. So let's roll it ahead to 8th level. You've got +5 Str and a +1 Greatsword, totally reasonable for 8th level. That's 2d6+6 vs 2d10 from Chill Touch.
I was assuming a longbow and firebolt.
You're choosing the worst case scenario for it. That's like assuming a whip on a champion.
If your in melee, use True Strike. Or at very least Poison Spray.
So does the Greatsword, thanks to Weapon Mastery.
Yes, but now you have access to a lot more abilities.
You can attack one person and cast friends to keep one guy off you while you focus on another (if you can convince your DM that your only "fighting" one target at a time).
Or turn 1 you attack and cast Create Bonfire, action surge, push them out and Lightning Lure them back in. Possibly the Sentinel feat and allies doing the same.
Or turn 1 you use mind sliver (+ silvery barbs) to setup for the wizards hold person.
turn 2 you action surge and critically hit them to death.
Or dig a hole with Mold Earth and push them into it.... might not be the best example to do in combat.
That's why I saying that without the weapon cantrips, EK doesn't actually gain anything from mixing in cantrips until 11th level.
Not sure why you would dismiss weapon cantrips.
Which is pretty dang late in most campaigns to start doing their signature trick.
Casting Shield several times a day is not exactly a bad signature trick for a fighter.
Or just use True Strike. Easy 1d6 damage bump, no matter what weapon your wielding.