Instead, the “best” use of the Hexblade becomes a dip, to give the curse, access to the shield spell and eldritch blast, shield and armor and especially that sweet cha-bonus to fighting, to *another class* (paladin and bard college of sword in particular). And that really bothers me :/
Am I wrong here? Did I miss mid-high level features of the hexblade that really make a difference? Is there an easy solution to fix the Hexblade?
Absolutely. The easiest solution is to accept that if you are playing a Hexblade it is because you wish to play the flavor of being a Warlock Hexblade.
Now, if what you really wish is to have the "best game mechanics available" to play a warrior + mage... then it doesn't matter what the flavor is. Take 1 level of hexblade mechanics, 19 levels of paladin mechanics, and then layer on top of it whatever flavor you'd like. If you want to call yourself a "warlock" even though you only have 1 game mechanic level of warlock features... that's fine! It doesn't matter one way or the other. If it matters that much... just go onto Homebrewery and write up a "Class write-up" for the warlock that lists what you get at each level using the mechanics of 1 dip in hexblade and 19 in paladin, come up with new names for the abilities you are using the mechanics for but not the fluff (so 'Lay On Hands' becomes 'Shadow Infusion' for example), then call it whatever class name you wish. Print it up, and you now have the class you wanted with the mechanics you wanted, with whatever fluff you wanted for it.
The whole point of having "classes" in the first place is to have generic and baseline stories that people can use as a shorthand to distinguish who they are for those players who don't wish to put in the time to "create" from whole cloth what they want. But at the end of the day, everything's just random names and fluff that are layered on top of generic game mechanics. The actual mechanics and math have no story. Any story that comes from a mechanic is only that way because we all collectively agree to accept that story for that mechanic. But those stories and names can be added to, changed, removed or whatever we wish.
So there's nothing wrong with using the game mechanics of a 19 paladin / 1 warlock hexblade and calling it strictly a "Hexblade"... just because you happen to think those particular game mechanics would be more fun to play in that combination and you like the story, background, and history of "the Hexblade". Don't feel guilty about it, and don't think you're having to "cheat" the system by creating this "new" build to get what you want. You want certain game mechanics, *and* you want your character to have a particular story? Take 'em both, wipe and re-write, and then go to town.