Would moving Hex Warrior’s benefits for pact weapons to Pact of the Blade itself improve balance?

Question

As described in my answer to another question, the Hex Warrior feature offered by the warlock’s Hexblade patron offers a kind-of-counter-intuitive upgrade to Pact of the Blade:

If you later gain the Pact of the Blade feature, this benefit [using Charisma instead of Strength or Dexterity for attack and damage rolls] extends to every pact weapon you conjure with that feature, no matter the weapon's type.

^{(Xanathar’s Guide to Everything description of the Hex Warrior feature, p. 55)}

I’ve often heard it said that Hexblade is a bit overpowered, but Pact of the Blade is a bit underpowered. It therefore occurs to me that we might be able to smooth things out a bit:

Would it improve matters to remove this feature from Hex Warrior, and add it to Pact of the Blade? Specifically, imagine Hex Warrior and Pact of the Blade are changed to read as follows:

Hex Warrior

[...] The influence of your patron also allows you to mystically channel your will through a particular weapon. Whenever you finish a long rest, you can touch one weapon that you are proficient with and that lacks the two-handed property. When you attack with that weapon, you can use your Charisma modifier, instead of Strength or Dexterity, for the attack and damage rolls. This benefit lasts until you finish a long rest. If you later gain the Pact of the Blade feature, this benefit extends to every pact weapon you conjure with that feature, no matter the weapon's type.

^{(Xanathar’s Guide to Everything with removed sentence struck out)1}

Pact of the Blade

You can use your action to create a pact weapon [...] You are proficient with it while you wield it, and you can use your Charisma modifier, instead of Strength or Dexterity, for the attack and damage rolls with this weapon. This weapon counts as magical for [...]

^{(Player’s Handbook description of Pact of the Blade with my addition in bold)}

Answers to this question should consider this question from two angles:

1. Does this make Hexblade more balanced with other patron options for Pact of the Blade warlocks? The goal is that Hexblade be less quasi-mandatory, and more of an equally-powerful option.

2. Does this make Pact of the Blade more balanced with other Pact Boon options? The goal is that Pact of the Blade be on more-equal footing than it was before.

In both cases, answers should address both whether the change is moving in the correct direction, and whether the change overcompensates and goes too far (e.g. that Hexblade becomes an underpowered option, or Pact of the Blade becomes an overpowered one).

1. _{Note that Hex Warrior retains the ability to use Charisma on attack and damage with the chosen weapon. Note that the chosen weapon is not a pact weapon, and that gaining Charisma to attack and damage with pact weapons is a separate ability—one I am moving to Pact of the Blade. Note that this means that warlocks with the Hexblade patron but not the Pact of the Blade feature see no change from this.}

Answer 1

This would improve Pact of the Blade, but not unbalance it

As you've pointed out, Hexblade warlocks would see no change from this, because they get to attack with Charisma for any weapon they touch (what I call their "hex" weapons, different from "pact" weapons), regardless of whether they choose Pact of the Blade or not at level 3. Should they choose Pact of the Blade, they get the same benefits as they would have done RAW. So I have nothing further to say about Hexblade warlocks.

You ask "Does this make Hexblade more balanced with other patron options for Pact of the Blade warlocks?", but given how the balance of Hexblade warlock does not change, it simply gives a benefit to Pact of the Blade that benefits all warlock archetypes, so from that perspective it at least doesn't tie someone who is interest in Pact of the Blade to the Hexblade archetype, as you suggested by calling it "quasi-mandatory".

On to Pact of the Blade itself, then. They can now use CHA instead of STR (or DEX if applicable) for their attacks. This makes it superior to its RAW state, since a warlock no longer needs to have a decent STR or DEX stat to make use of Pact of the Blade; now they only really need a decent CHA stat. Does this unbalance Pact of the Blade?

Comparison to Eldritch Blast

Your suggested change lets a warlock use CHA to make attack and damage rolls with a weapon. They can already do this via the Eldritch Blast cantrip + the Agonizing Blast eldritch invocation. In either case, it's 1d0 + CHA mod (assuming a weapon with 1d10 damage).

When the warlock hits level 5, that can increase to 2d10 for the cantrip, but if they pick the Thirsting Blade eldritch invocation, they get two attacks, effectively increasing their weapon attacks to 2d10 per round as well. Both methods of attacking involve separate attack rolls and potentially separate targets, so there's no real difference (unless the warlock picks a greataxe for 1d12 or a greatsword for 2d6, but that's only at most 2 more points of damage, hardly unbalancing). At 11th level or higher, Eldritch Blast goes up to 3d10, leaving Pact of the Blade behind.

However, Pact of the Blade can somewhat catch up at 12th level, if you pick the Lifedrinker invocation, which allows you to add necrotic damage equal to your CHA modifier, so that's another +10 damage compared to the Eldritch Blast's extra 1d10 + 5 (assuming you've increased your CHA to 20 by this point). This also somewhat helps it to keep up with Eldritch Blast. Of course, at tier 4, Eldritch Blast jumps up again, now dealing 4d10, and Pact of the Blade has no hope of keeping up with that.

And that's something all warlocks can do (since every warlock ever has Eldritch Blast and Agonzing Blast, right?) so at the moment it all seems balanced.

Melee Combat and Pact of the Tome

The only real difference is that Eldritch Blast isn't as useful if you have enemies in your face. Then you have to make your ranged attack rolls with disadvantage. That's where Pact of the Blade becomes the stronger option. However, and this is where I start making comparisons to other pact boons, Pact of the Tome already has solutions to this problem.

If you pick the Shocking Grasp cantrip via Pact of the Tome, you are making a melee attack roll that does xd8 on hit. This is weaker than your Pact of the Blade, true, but it does also prevent reactions, which means you can run away (potentially Eldritch Blasting them next time if they can't run as fast as you).

Furthermore, there's the Shillelagh cantrip. Given that it counts as a warlock cantrip for you if picked via Pact of the Tome, this effectively matches your Pact of the Blade, 1d8 + CHA. Your Pact of the Blade is still stronger, since you can pick weapons of > 1d8, and via Thirsting Blade you can attack twice, but these are only relevant in scenarios where you're up close, and Pact of the Tome offers other benefits (such as different cantrips like Sacred Flame, Guidance, etc, which give benefits in other situations that Pact of the Blade does not).

Summary

Given that non-Pact of the Blade warlocks will choose to hang back and use Eldritch Blast anyway (which I deem as balanced compared to your Pact of the Blade), the only way that this Pact of the Blade is stronger is that you can get out of melee situations better, but then, isn't that the point of Pact of the Blade anyway? And, at the very least, warlocks with Pact of the Tome, depending on their cantrip choices, can also find ways out of melee combat.