The HexBlade spam is ridiculous. Test your players and ask them if they read these parts:
"You have made your pact with a mysterious entity from the Shadowfell—a force that manifests in sentient magic weapons carved from the stuff of shadow. The mighty sword Blackrazor is the most notable of these weapons, which have been spread across the multiverse over the ages. The shadowy force behind these weapons can offer power to warlocks who form pacts with it. Many hexblade warlocks create weapons that emulate those formed in the Shadowfell. Others forgo such arms, content to weave the dark magic of that plane into their spellcasting. Because the Raven Queen is known to have forged the first of these weapons, many sages speculate that she and the force are one and that the weapons, along with hexblade warlocks, are tools she uses to manipulate events on the Material Plane to her inscrutable ends."
To me it seems such a pact would never be granted to a good aligned PC (unless to subvert the PC) nor would any good aligned PC search them out. Using the tools to "manipulate events on the Material Plane to her inscrutable ends" to me means the hexblade probably wouldn't play well with others.
I am not even sure the Pact creature would continue to grant the Pacts benefits if you multiclass just to dip as:
"A pact can range from a loose agreement to a formal contract with lengthy, detailed clauses and lists of requirements. The terms of a pact—what a warlock must do to receive a patron’s favor—are always dictated by the patron. On occasion, those terms include a special proviso that might seem odd or whimsical, but warlocks take these dictates as seriously as they do the other requirements of their pacts. Does your character have a pact that requires you to change your behavior in an unusual or seemingly frivolous way? Even if your patron hasn’t imposed such a duty on you already, that’s not to say it couldn't still happen."
That seems to me the DM dictates ALL the terms and change them at ANY time for ANY reason. It is certainly within DM bounds to withhold Warlock features and benefits until you "show your devotion to me" i.e. gain more levels in the Warlock class.
So it seems you are zeroing in on one specific patron for your games - thats certainly a lot more "for setting consistency" than "because i said so" than banning all warlock multiclassing. Cannot speak for your setting and the limits you choose to set into its most powerful operators
but for my worlds i can answer some of these...
1st Do the players need to read the bits about the new classes and patrons etc? yup, or at least, when we have that warlock-patron/player-gm pre-choice-talk i will make it clear to them how i run the patrons and how they vary quite a bit between one pact to another. Just like with clerics and to lesser extent every character alliances and deals are two-sided. The one's key to a class, race or background - even more so.
2nd Whether the Raven Queen, hex-patrons and hexblade could offer their pact to good aligned individual - of course. Whether or not they could have warlock's beholden to them that did play well with others, of course. Even an outright evil god/patron could... and relish in using them to serve their purposes - like say perhaps being very effective tools to work with others to weaken the patron/gods rivals. Right? Evil does not play well with others" includes at times "other evil" and why expend loyal evil deinzens when you can expend disposable gooders who owe you? The very powerful beings we are discussing here may not be as limited in my worlds as in yours - thats fine of course.
But the "one evil faction" using and backing "goodly do rights" to go kill the opposition is old classic solid staple storylines with plenty of analogs in real life and history. not sure why a Gm would want to limit that and ban it out of their games.
3rd As for the idea that a patron would somehow "punish" the pawn for gaining other levels in other classes - well, i supposed some might feel that way - but again if they see the pawn as a tool for being used - why object to your tool getting better by a means that doesn't need you to provide more power? other than maybe vanity sake, why not let your pawn gain ten levels in fighter and be an even better pawn? They still want what you give them and use it every day so... you still have them on the hook.
hold your big leverage for when they actually refuse to do something you ask... not when they just get more powerful on their own, right? makes more sense.
And yes... the discussion between player-gm about the warlock-patron and what that means is vital to the class - as is so very highlighted in the main intro to the warlock class.
But, that would apply - most of what you describe here in fact - that all applies whether multi-classing at all or primary-classing.
So this really seems more like a series of "trouble with the warlock" items than anything specific to multi-classing.
Right?
The good character hexblade - not just related to multi-=classing?
The patron hold back powers, patron might change up terms etc - multi and single class both right?
Sounds like you dont like warlocks or maybe hexblade warlocks. maybe that should be its own thread separate from multi-classing?