I have to agree: the Life Drinker invocation comes waaay too late to be balanced vs. Agonizing Blast, and I have no idea why.
Its there to make Eldritch Blast equivalent in power to a longbow user without feat support or Fighting Styles. When you get right down to it, someone using a Rapier is going to be doing less damage than someone using a longbow without more support. And that's exactly what happens. The problems are exaggerated for several other reasons, however.
Life drinker is the equivalent of the Paladin's Improved Smite. The idea is that, for weapon based classes, you get a boost in damage around level 11 or so to keep up with the dedicated spellcasters.
Fighters get their second Extra Attack. Paladins get Improved Smite for extra 1d8 per hit. Valor Bards get Magical Secrets to steal Smites or Bow spells, which are really good with the higher level slots. Favored Souls can consistently have Haste or Elemental Weapon up, plus bonus action cantrip damage that scales. These are milestones. Moving Lifedrinker around messes up the milestone progression.
The big reasons why the hexblade falls behind is due to being MAD (DEX/STR for hitting physically, CON for Concentration checks, CHA for spells and Lifedrinker), lack of good feat support, AC woes, dependance on Hex's Concentration, and lack of variety in
viable weapon choices without multiclassing (yes, they can pick any weapon, but warlocks by default need DEX for defense too much to sustain STR weapons).
Simply adding in more damage doesn't address these problems, and, in fact, causes imbalance. Dipping one level of Fighter helps with a lot of the above problems; adding in more damage simply makes the Fighter 1/Warlock X that much stronger while still leaving problems for the non-MC blade.
Life drinker is meant to be a replacement for getting a 3rd attack/cantrip die around level 11. Unless you make Hex incompatible with bladelocks (which might not be a bad idea, given the concentration issue), a bladelock would absolutely have by far the best possible sustained damage in the game until level 11.
I'm going to say that you'd be better off making Hex a non-Concentration spell with Blade'locks. They're based off the old hexblade class, after all, its a huge part of the class flavor.
Actually, what I did is make the spell "demi-concentration." When you lose Concentration, the spell doesn't end - it just doesn't affect a target anymore. You can reapply it the next round. Still lasts for the full duration. This way, we're looking at preventing the stackable buffs, more applicable outside of combat, and more fun.
But, yes. Putting Lifedrinker so low would create issues when someone min-maxes.
As it is, bladelocks are absolutely competitive damage dealers if they wield a 2-hander, have high STR and CHA, and can maintain Hex. Yeah, that's a lot of 'ifs', but I think the solution is to make the 'ifs' easier, not mess with the progression.
Hmmm... I personally went with a Finesse weapon for my Pact Blade, but focusing on DEX has lots of other benefits (Initiative, high AC, good saving throw, etc) so maybe I shouldn't worry about not having a 2-handed weapon.
As for Hex, well no, I think I'd just as soon keep it, "concentration issue" or not!
Part of the issue is that Heavy weapons are flat out superior to Finesse weapons. DEX-based weapons usually end up keeping pace with the two handed stuff because of things like the right Fighting Style, Dueling with shield mastery, or class support from the Rogue, Monk, etc.
The Warlock just isn't getting that support to maintain a duelist style. Using a bonus action to make an attack is crap without the TW FS, and only Polearm / Great Weapon Mastery give bonus action Cleaving. Other duelist options are shields, which aren't standard for the warlock either.
