I think this is a generally good idea, and well-thought-out. In particular, I think your analysis of the Hexblade's design purpose is spot-on:

Quote Originally Posted by Segev View Post
It is fairly clearly meant to complement the Pact of the Blade, as it is a bit clumsy when combined with any of the others. And while it can be made to work, the notion of "sentient weapons" as a Warlock Patron is a bit weird in and of itself. It is likely that its clear complementary status is meant to be a kind of salvation for the Pact of the Blade not working quite right due to pulling the Warlock towards melee when he clearly isn't designed for it.

In addition, a couple of the abilities feel more like "crap, Patrons need something at this level; what do we give this one?" than solid thematic links.
I also agree that something needs to be done to bridge the gap of "I'm a caster for the first two levels and then suddenly I'm in melee at level 3". You use Shillelagh, but what if we just imported a tiny bit of Pact of the Blade directly into the base class at level 1? Make some minor use of weapons into A Warlock Thing?

I'm thinking either (A) let all Warlocks use Cha with weapons they're proficient with, (B) let them use it with specific weapons based on the Patron. Since they start with simple weapon proficiency, option (A) is basically what you're getting at with Shillelagh, except this allows ranged weapon too. Option (B) would be a little more thematic, and would let you emphasize the flavor of certain classes of patrons (as well as their martial capabilities).

Example:
- Fiendish Patron: Mace, spear, greatclub
- Fey Patron: Shortbow, sickle, quarterstaff
- Great Old One: Dagger

Notably, none of these match Agonizing Blast's damage output, so Warlocks who don't go Pact of the Blade aren't necessarily more powerful with this addition. The major consequence is that Pact of the Blade Warlocks can start using weapons from level 1, but the actual Pact at level 3 still has an impact by opening up all martial weapons.

Speaking of which, we might as well roll the martial weapon proficiency into Pact of the Blade to close the "not proficient with this magic weapon" loophole.

That just leaves the question of whether we should put medium armor and shield proficiency into the Eldritch Armaments invocation tax, or just add those to Pact of the Blade for free. Personally, I think medium armor and shield proficiency is more than worth an invocation slot, and I'd actually add a Pact of the Blade requirement to it. Otherwise there's little incentive for even caster Warlocks not to armor up, and the whole point is to make Pact of the Blade work as a weird "turn this caster into a fighter" class path.

(Your implementation of Hexblade's Curse looks good, I have nothing to add on that one.)

Thoughts?