The game is not broken. We do not need to fix it.
Hexblade is fine.
It was actually fine. I played one, and then I played a Hexblade later. Both were very enjoyable.
My Great Old One Pact of the Blade PC used Armor of Agathys, Hex, Misty Step, Mirror Image, and other spells that didn't care about what his Charisma was at first. It was more fun to play him, I'd say, but that was likely due to the DM's fondness for Lovecraft mythos and how well he wrote my PC into a central role in the campaign. The Hexblade I played had a patron that wasn't really a sentient weapon ... it was a dark Sauron type figure that wanted to make a magic weapon.
Before my Hexblade I had played another Warlock, of the Pact of the Blade Warlock with the Great Old One Patron. He had the Sage background and had originally been a mathematical prodigy, and at 25 years old was the youngest-ever professor of mathematics at the prestigious University of New Aberdeen (an ancient establishment much like Oxford.)
But one day, while researching old books for possible insights into a solution for a difficult mathematical proof he was working on, he stumbled across an utterly bizarre and ancient tome that he had never even heard of before:
A Treatise on Hyper-Spatial Calculations in 5-Dimensional Spacetime.
Someone (or some
thing) had intentionally planted this eldritch tome among the otherwise normal mathematical treatises in the University library, and this young mathematical prodigy became utterly obsessed with it. He read it from cover to cover, virtually inhaling its contents, and was just barely able to grasp the concepts presented in the book due to his innate mathematical skills... which caused his mind to make contact with Yog-Sothoth, and his continued obsessive study of it unintentionally forged a Pact with the Outer God, rendering the young man (Professor Eldred Eldridge, the most perfect name for a Great Old One Warlock I could think of) stark raving mad, which lead to him writing a rambling, nonsensical, 3,000 page mathematics paper (which itself was a minor Mythos Tome) before the being locked in a madhouse due to his insane behavior for the next three years.
After three years he escaped during a fire at the madhouse, but by this time he had recovered enough of his senses to pass as sane most of the time, and began a wandering adventuring career. He devised a method of creating a staff-shaped area of spatial-distortion for use in combat (IE he took the Pact of the Blade) and came to realize that his mathematical studies had accidentally stumbled upon a form of magic which was unlike Wizardry, and that he was somehow mentally connected to some form of vast, inhuman consciousness (Yog-Sothoth, the Outer God connected to all of spacetime) which continuously whispered to him in the dark recesses of his mind.
He was a fascinating character to play; Chaotic Neutral (while trying to remain
Good,) always battling to remain in control of his mind, but slowly losing the battle. He had no idea what he was going through, as he had never had any magical training, although he did realize that he had stumbled upon some kind of magical secrets, and he was slowly attempting to conduct magical research into what possibly could have happened to him.
Unfortunately that campaign group fell apart around 7th level, and when we started a new campaign soon after it was with new characters at 1st level. I always wished I could have continued that character, as he was just so damn cool, and he was
the character I had been wanting to play ever since I first read the D&D 5th Edition PHB and saw that one of the options for Warlock Patrons was the Great Old One, with Great Cthulhu actually listed as one of the possibilities. I though "If Cthulhu, then why not Yog-Sothoth, an Outer God that was overwhelmingly worshiped by cabals and covens of Wizards of Witches (and Warlocks
are absolutely Witches, with Warlock magic totally being
Witchcraft.)
He was an incredibly fun character to play, but he was
not at all overpowered. The Pact of the Blade was very cool and allowed for some neat conceptual ideas as to the origination of his Pact Weapon, but it hardly made him a combat monster.