IMO. If one takes True Strike, Shillelagh, and Polearm Master on an EK by level 7 then I think that version of EK can do very good damage. At that point just let your first spell be a control spell along with Shillelagh and forget wrathful. Then follow up with PAM attack routine the rest of the battle.
The main problem with PAM that early is it boosts Strength or Dex while Shilleleagh is using Intelligence.
Going with a straight standard Fighter PAM build to Strength 20 does substantially better damage at level 7 leaving Intelligence at 16, especially when you consider you don't pay the bonus action tax.
Not clear to me if Shillelagh should overwrite the d4 on the polearm master attack. I'll assume not for now. That comes out something like (assuming 60% base chance to hit):
Attack Action
attack 1: d10+4(mod)+2(dueling)
bonus action attack: d4+4(mod)+2(dueling)
attack 2: d10+4(mod)+2(dueling)+3.5(true strike)
Shilleleagh PAM vs Strength PAM
attack 1: d10+4(mod)+2(dueling) vs d8+5+2 (tied, but with a slightly better chance to hit with strength)
attack 2: d10+4(mod)+2(dueling)+3.5(true strike) vs d8+3+2+3.5 (Shilleleagh 2 DPR ahead)
bonus attack round 1: 0 vs 1d4+5+2 (Shilleleagh 9.5 DPR behind)
bonus action attack: d4+4(mod)+2(dueling) vs d4+5+2 (Shilleleagh 1DPR behind every round after 1st)
Your true strike attack will have a good chance of having advantage due to 2x topple attempts. ~59%
But if you are doing this it is better with just getting strength, and you get 2 attempts on the 1st round.
I think I'm more impressed with this version than your Wrathful Smite version. Especially since it better pairs with spells like Web or Tasha's (better control than Wrathful Smite provides, and better chance to land on that all important round 1, since they don't depend on any attack hitting to be able to use them).
Wrathful Smite is far better in play on an Eldritch Knight because it is not concentration and it does not take an action to cast and it is generally a more difficult save to make.
Wrathful smite is cast on a hit which comes with part of an attack so the target always has disadvantage on that save (after level 10).
Control spells are most effective early in a fight (with Wrathful Smite ideally at range, but still effective close), Web and THL are generally more effective spells than Wrathful Smite, but casting them on round 1, when they are most effective, means enemies do not have disadvantage unless you action surge and attack them first. They are also concentration spells, which wrathful smite isn't, meaning it can't be broken by damage and you can use it more than once even if it or another spell is already going.
IMO, tactical master on turn 1 is mostly overrated if your turn 1 is mostly going to be control spell and don't get adjacent (wanting to trigger the PAM reaction attack).
The reason I said Tactical Master was so useful with wrathful smite is due to the movement limitations imposed by the Frightened condition.
And then some encounters you won't need to start with a control spell (this version of EK has much better damage in that situation).
The thing with Wrathful Smite is you have a control spell while also having an attack, you don't have to give up one for the other and they always have disadvantage on the first save (after level 10).
To put this in perspective the shillelagh EK might do something like
Round 1: Web + Shillelagh
Reaction PAM attack
Round 2: Attack, bonus action attack, truestrike
Round 3: Attack, bonus action attack, truestrike
I don't see the Wrathful Smite focused EK matching turns like that at all. If he matches the Web then he's down damage. If he matches the damage then he's down control. It's worth noting that 2024 wrathful smite differs from 2014 in that the creature needed an action to attempt the save again in 2014, but no longer does in 2024.
THL is a better comparison because it is a single target and a 1st level spell. I also think in the 2024 rules, upcast THL is generally a better 2nd level spell than Web is. Not always but usually. If you compare to THL on 1st round with and without action surge:
THL: The enemy makes a normal saves or become incapacitated (concentration)
Wrathful Smite: Do around 20 damage total and then save at disadvantage or become frightened.
With WS you can repeat on round 2 and round 3 on other enemies because it is not concentration.
If you use action surge you can actually get off two control spells with WS while still attacking (once a day):
THL: Action Surge-attack then action-THL with disadvantage
Wrathful Smite and THL: Action surge, split your attacks, bad guy 1 Wrathful Smite with Disadvantage, bad guy 2 THL with disadvantage (assuming at least 2 hits)
The best Nova of the Eldritch Knight I've seen in tier 3 is actually with both Fey touched and Shadow Touched and using the following combo all in one turn: Action Surge (attack), Bonus action (wrathful Smite-disadvantage on save), Action (Dissonant Whispers-disadvantage on save), Warcaster spell AOO all on the same enemy
With both feats you can do that twice a day with 1 short rest using a Cantrip with the Warcaster AOO or once a day using a third leveled spell with the Warcaster AOO. In 1 turn it comes out to War Magic attack action, +4d6 damage+frightened+moved back their movement + lost reaction and you still have one more spell you would have cast on them.
