One thing that you need to look at is how MAD the class is. For instance, with the Bladesinger getting +INT added to Concentration, AC and damage they are not MAD at all. They can pump INT and not worry about the rest as much. A blade-lock as written is crippled by MAD issues.
However I read the Arcana Unearthed article on the Warlock Hexblade as trying to fix the shortcoming of the blade-lock class. The Hexblade gets Medium Armor, Shields, and uses CHR for attack and damage modifiers with their pact weapons. That moves them closer to par with the other classes here I think. In my house rules I make this a feature of the Pact of the Blade so that all patrons can be have viable blade-locks.
Putting the Blade-lock's extra attacks, HP boosts, and bonus damage in the Invocations section though is sort of necessary. The Invocations allow you to build your Warlock as an infiltrator, warrior, ranged blaster, etc. It's very flexible. But you do have to choose. If the Blade-lock got Extra Attack, +X weapons, automagic mage armor, etc. AND Invocations on top of that they'd be ridiculously better than Valor Bard or Bladesinger.
I think they should have a basic extra attack built in, but agree that a bunch of their stuff should be in invocations. If they had a few different defense-focused invocations, for varying armor types, they would be able to make the choice of only grabbing the Light-armor (Armor of shadows in this case), and be able to choose other things as well. I also think the Life-drinker invocation should remain, because it feels right that it is an invocation. Basically, the only bug I see is the extra attack being made an invocation. That is just my opinion though, others might want the three to be more similar classes.
This is a very timely post. I have a player that is asking to switch from a bladelock to the UA Hexblade. We're working out the details on what to do for the level 14 feature. We removed the level 6 feature, Ghost Hound, because it lead to using Eldritch Blast as a primary attack, and we both wanted to force the subclass down the melee path. We bumped the level 9 feature to level 6 and the level 14 feature to level 9.
As suggestions for the level 14 feature, I looked at the Bladesinger, Champion fighter, and War cleric.
The greatest challenge with the hex blade is the lack of a need to manage resources. HP is one resource that is used by fighters and other martials. I feel the Hexblade should also be put into the position of managing that resource, but the HP recovery is to outstanding when the warlock takes the invocation that allows moving the hex to a new creature when the previous creature dies.
I like some of the hexblade, the parts that make it a better gish, but dislike a lot of it too, like the Curse. I am not a fan of Hex/Hunter's mark because they are bland, and most often amount to +damage. I would rather have seen the crit 19/20 made into an Invocation for the Blade pact, with something like a 9-15th level requirement, and the rest scrapped. I like the proficiency in Medium armor and shields, but don't feel it is required to make the bladelock function on the same level as the other two. I think they should get something else like the Armor of Hexes, but not that, because that seems like a really odd mechanic. I would just copy from the Bladesinger and make it +Cha to AC, with a limit of +3-4 since it would be always-on instead of a limited resource.
I think a 14th level +cha to AC (max 3) and a built-in extra attack would level the field. Either that, or there should be multiple non-stacking defense boosting Invocations. One that gives the equivalent of heavy armor (I would say as an action), one that gives a Shield pact-weapon (Probably as a bonus action), and they already have mage armor to cover a Light armor equivalent. This gives flexibility to building your preferred Bladelock, the way it should be, instead of having a single basically-required invocation if you want to actually play in melee.
Factoring in my preferred changes, extra attack and +cha to AC (max 3) I will check this out again.
Attacks: 2x whatever weapon they choose+5 (+10 with an invocation)= minimum damage of 12 (22), Maximum of 34(44), which seems alright in comparison. The maximum is a bit higher than Bard with a rapier, but Bard also has access to things like Shield or Haste, so Valor can get that +2 AC and 3rd attack in as well. As a gut feeling, they are roughly equal.
Armor of Shadows: 13+dex(Mage armor), +Cha (Max 3), max AC of 21. Higher than a Monks max AC, but does not require as much investment since you could just stop at 16 Cha. I might limit that to a max of 2 instead.
Light Armor: Max of 12+dex+Cha(3)=20, more within bounds, but still high considering someone like a Rogue will be a few points lower. Although, rogue also has high DPR, so I am not sure how to judge this. I still prefer the 2 limit at this point.
Medium armor: Max 15+Dex(2)+Cha(3)= 20, higher than medium armor characters with a shield. Too tanky I think.
So, after that flow-of-thought style running of numbers, I would rather see +cha (max 2) to AC, and maybe something else, since a +2 to AC feels pretty small at level 14. This might be where I would include something like the third rider of the Hexblade curse.
+cha to AC (Max 2)
When you kill an enemy with your pact weapon you regain hit points equal to your Warlock level+ your Charisma Modifier.
That feels like an alright boost at 14th, right?
Sorry for rambling...