Good stuff! I think the capstone needs work, since this essentially obviates two weapon fighting, GWM, PAM and Crossbow Master, and clashes with Shield Master.
I came up with divine subclasses for Fighters and Rogues some time ago, you may want to try them out:
http://www.giantitp.com/forums/showthread.php?423152-Divine-Subclasses-Fighter-and-Rogue-(PEACH)
Thanks for the link, I'll definitely look over and see if you give me any ideas. That said, the 'capstone' is literally a copy of Eldritch Knight's level 18 bonus. Please explain how it 'obviates' any of the items you mentioned, I just don't see it. It reduces their power level slightly, but it's not like a Crusader would have enough spell slots to cast a useful spell every single turn. Or would even want to! TLDR for the rest: potential minor DPS boost depending on build, but the spell slot usage makes it unsustainable long-term. (And of course, level 20 negates said boost)
Lets do some math. I'm going to assume that at level 18, a fighter has a +5 in their relevant attack stat(s), just to balance everything out.
Inflict Wounds at level 4 would do 6d10 (average 33) damage, which is nice. Add in 1D8+5 (average 9.5) from a one-handed weapon attack for a turn-average of 42.5. Compare that to three regular attacks, doing 28.5, and I'll freely grant it does a touch more damage. Except by level 18, a fighter can reasonably be assumed to have taken either a fighting style or a feat to improve that. Even a simple dueling fighting style increases it to 44.5 vs 36.5, quickly closing the different. The more damage you get out of your weapon attacks, the more that gap moves in favor of the weapon attacks. A +1 weapon makes it 45.5 vs 39.5, with the weapon attacks having an improved probability to hit that moves it even further. +2 makes it 46. vs 42.5, +3 moves it to 47.5 vs 45.5. Oh, wait, maybe the fighter has a flame tongue instead of a flat +x. Or maybe instead of a one handed weapon, they're using a 2H weapon and the math is all wrong.
I started out simple, assuming a +5 to both wisdom and strength and no modifiers. But the more you move away from that baseline assumption, the more it breaks down. And that's assuming spells were at will, which they aren't. They use spell slots, a sharply limited resource. You get one -- count it one -- fourth level spell slot. The fighter will probably want to save that for other things. Just like a Cleric, Inflict Wounds is
ok, but it's a filler. A high level Cleric doesn't use Inflict Wounds as a baseline, they use Spirit Guardians. Or Death Ward. Guardian of Faith, Blindness/Deafness, even Bless. The list goes on and on. And that's just combat utility. Sending. Freedom of Action. Remove Curse! All great options that might be chosen to round out the fighter's abilities rather than try and spec into the combat stuff they're already awesome at.