This is pure nonsense; all three Pacts in the PHB have their own dedicated invocations which are all but required for Warlocks who take that particular pact. The Blade Pact is no worse off than the others in this regard.
First, I'll respond as if you are right about the other two books requiring just as many Invocations.
The blade Pact warlock uses those Invocations to only be as good as using Eldritch Blast, is still behind EB with Agonizing and Repelling Blast, while the others still benefit from EB, and their Pact boon genuinely adds to the character's efficacy. And their invocations do more, IMO.
second, I'll address that idea that all three equally need their Invocations.
Blade Pact boon does almost nothing. It's practically a ribbon. The other two aren't close to ribbons.
Chain: Free ritual use of a 1st level spell, which means it doesn't use a spell slot. Doesn't count against spells known. Expanded familiar list. Familiar can attack using one of your attacks when you use the attack action. A solid class feature, all on its own.
Tome: 3 extra cantrips. From any class, using your casting stat. So, includes shillelagh, which in turn obviates a lot (not all, but a lot) of what the blade Pact feature even does, and shillelagh lets you use cha for attack and damage. List also includes SCAG cantrips, EE elemental cantrips, spare the dying and other concept specific cantrips. It's a lot of added versatility.
Blade: lets you effectively ignore issues of weapon proficiency. Costs an action to summon the weapon. Can't have ur weapon taken away, which isn't an advantage over...ya know...cantrips.
Being able to use a polearm in one fight, a rapier in another, and a hammer in another seems cool, but the feature doesn't really synergise it well.
Especially when switching requires dismissing the weapon and creating a new one as an action. And if you specialize to get the real potential out of any given weapon type, you've given yourself a disincentive to even use that versatility.
The weapon is magical...ok, so is shillelagh, and IT lets you use your casting stat, instead of having to pump dex or str.
OK, so next let's look at the invocations in the PHB for each boon.
Chain:
Voice of the Chain Master. OK, this is cool, and I don't know why you wouldn't take it as a warlock. If you're focusing on Eldritch Blast spamming as your main strategy, this takes a back seat, but still, it's cool, and if you aren't doing that I'd recommend this right away. But, I wouldn't care about it at all if I were optimizing my warlock character. It wouldn't even enter my mind to bother with this, when there are so many stronger invocations. I want this one purely for fun/cool factor, not efficacy. Miles and miles away from being required.
Chains of Carceri: Interesting case, because it is good enough that it makes Chain pact more appealing, if you expect to get to level 15, but it doesn't interact at all with the actual feature. literally at all. certainly doesn't make the feature more powerful, it's about in line with the options available to everyone, this one is just thematically tied to being good at binding creatures, and thus the chain pact.
So, yeah, chain pact does what it says, no need for any invocations to bring it up to speed. A chain lock will be fine choosing non chain invocations every time.
Tome:
Book of Ancient Secrets. I love this invocation. Seriously, I want rituals to be part of the Warlock base class, because I think it's silly that they aren't ritualists to begin with, but I'll ignore that because this invocation also gives you two lvl 1 spells from any list as rituals, which is nice. It's a logical extension of what the Tome feature does, but doesn't do anything to like...make the Tome feature work better, or anything. The Tome feature itself still stands on it's own. Definitely would question a person who took Tome but didn't take this, however. bit of a wash, in this discussion. pretty far from "all but required", because the feature stands alone just fine without it, but also no real reason not to take it, because it's really good.
That's it for PHB invocations for the Tome pact boon.
Blade:
Thirsting Blade. Should just be part of the Pact Boon. It is literally necessary for the blade build to work as intended. SCAG mitigated the issue by giving us scaling weapon attack cantrips, but that still leaves the Blade lock behind other GIsh options in the game that get something like Extra Attack built in, unless the blade pact takes this invocation, making it "required" still.
Lifedrinker. Adds Charisma Mod damage to attacks with Pact Blade, requires level 12. So, this one is the replacement for other build's level 11 damage boost, I assume. So another invocation tax.
And here is where things get more subjective. The warlock isn't a tough guy, stock. 1d8 HD isn't bad, but it means the Warlock, like the Rogue, has to rely on guile and mobility to survive hitting things with a stick. Which means, he needs more invocations dedicated to that cause. I'd say that at least one of the following is needed for a Blade-lock to reliably survive being in melee.
Fiendish VIgor: False Life as a cantrip. Shores up those HPs.
Armor of Shadows: Always on Mage Armor, which is basically a +1 to AC over what the Warlock has proficiency in.
One With Shadows: Invisibility any time you're in shadows. doesn't make you hidden, but makes hiding easier, and make hitting you harder even if they know where you are, and make it impossible to target you with many spells. Good for all warlocks, necessary for warlocks that don't do anything else to improve their defenses.
Meanwhile, other warlocks can take Agonizing Blast, Repelling Blast, Eldritch Spear, and make their "basic attack" equivalent much more powerful than the Blade-lock's melee attack, from impressive range.
Or, if they don't like EB spamming, do any number of other things, and take invocations that increase their spellcasting, let them fly, read all languages, or see magic at will. And can take more of them than the Blade-lock.
And even after UA is allowed at your table, let's say you take one of the new "pseudo-smite" invocations for the bladelock. So, now you can do a smite. Cool. You can invest more character resource into being as useful as the other pacts are before considering their invocations.
Even picking up Hexblade, why would I saddle myself with the blade pact? I could instead be a Hexblade with a cool grimoire that gives me extra spells and rituals, or a hexblade with a pet. The Hexblade doesn't obviate the blade pact, but it also doesn't require it, so... the question remains the same as it was before that UA article: why should I bother with the weakest pact boon when I can accomplish it's goals without it?