Shilleleagh does 3 more damage at level 7 than a Rapier without Vex.
Rapier attack action 19 Intelligence, 16 Strength:
Attack 1d8+3, Truestrike 1d8+1d6+4, Total damage 4.5+3+4.5+3.5+4=19.5
Shillelagh attack action 19 Intelligence:
attack 1d10+4 Truestrike 1d10+1d6+4, Total damage 5.5+4+5.5+3.5+4=22.5
22.5 is 3 more than 19.5 and that is without considering Vex and without using a bonus action for that 19.5
Vex is not a flat bonus, statistically, its damage increase depends on the number of attacks you make against a single foe and the base chance to hit that foe and it carries over from round to round, so it is not only the first round, hitting with your last attack on the first round gives you a better chance to hit on the second round.
If you assume a base 60% chance to hit with the Rapier and vex your mean damage is as follows assuming you attack the same target. This includes critical hits:
1st round: 14.3
2nd round: 16.4
3rd round: 16.5
Three round total: 47.2
The mean will keep increasing very slowly after that every round as long as you attack the same target. When you switch to a new target it drops to 14.3 and starts over.
With a Shilleleagh using Topple against a foe with a +3 save (DC15):
Round 1: 15.3
Round 2: 15.3
Round 3: 15.3
Three round total 45.9
If you are a melee character it matters a lot and they use it all the time in the 2024 games I have played. You use it to close in melee, either after the enemy near you moves/dies or on the first turn if you start more than 35 feet away.
With 1 use every short rest and 3 to start the day it is generally one use per battle or more, on days with few fights it is a lot more than one use per battle. You say it is a limited resource, but with 2 short rests that is 5 bonus actions per day to use it at 7th level, 6 at 11th level where your Shilleleagh damage really starts to shine. If you actually use it that is taking away from your other bonus actions, including Shilleleagh and PAM when you get it. If you don't use it then it really isn't limited is it?
Also for most PCs it would be 35 feet away, not 40 to close into melee range with a Shilleleagh.
The entire build I commented about was a Wrathful Smite build, but even you don't do this you still need to boost Intelligence early if you want to get max use out of Shilleleagh, which means not taking PAM until late. Truestrike is available at level 3 and at level 7 Truestrike is your most powerful attack.
If you are allowed 2014 spells then Shadowblade is available at level 7, but it is very limited use, it is concentration, it doesn't work with Truestrike because of the material component and it uses Dexterity or Strength, not Intelligence. At level 7 compared to a Rapier with Triestrike/Attack it is 4.5 points more DPR for 1 fight at the cost of your highest level slot. At level 11 it uses your highest level slot and is the same damage as a Rapier with Truestrike-Attack would be.
From a Concentration point of view your damage is better if you get Hex or Hunter's Mark through Fey Touched, than it is with Shadow Blade. That uses a lower level slot it lasts longer and it allows you to continue to make one attack with Intelligence.
Saving slots for shield and defenses is fine, but at level 10+ you are really missing out on the power of the class with Eldritch Strike to make someone save at disadvantage on turn. If you are running a high Intelligence Eldritch Strike is awesome and Wrathful Smite is one of the best spells to use with it. So are Dissonant Whispers and Command. Even if you are not branching out with feat spells, on the Wizard list there are 1st level standouts that work great combineing Action Surge and Eldritch Strike. Tasha's Hideous Laughter and Cause Fear are two of them. With extra attack you can even upcast these and get multiple enemies saving with disadvantage.
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