There's so much wrong in that assumption.

1. The largest force in the world has almost sole control over Sea Stone Production. Sea Stone is a liability to their own forces, why would they mass produce it? It destroys their own power by proliferating it or allowing others to do the same. Why would you let someone hand out tools that basically make your top people useless? You don't.

2. Sea Stone is rare and it's more useful for other things. Containing Devil Fruit Users is more important than being able to fight them. Because for one thing Devil Fruit Users are rare in the world, not rare in the story. Why spread a lot of weapons to fight a foe that you can fight via other methods? Logia are explicitly the most rare of all Devil Fruits (Under Mythical Zoan but w/e), wasting Sea Stone on the possibility of one is a terrible terrible tactic.

3. Haki. Haki is something people can use and doesn't require resources, time or special tools.

4. Calm Belt Navigation. We're told that's where the majority of Sea Stone goes into. Bottom of boats so the Marines can have unparalleled navigation abilities around the world.

5. Vegapunk. We're told that he's the one who created the idea of coating the bottom of the ships the Marines have with Sea Stone in the first place and he discovered how to manipulate it in the first place. Research the World Government undoubtedly wouldn't want to share.
Since none of this actually adress my conclusion then i am going to conclude that it is in fact correct. If you want to disprove it then you need to start over, and come up with convincing arguments for why widespread Seastone weapons would not significantly change the power dynamic in the world of OP.

It's rare enough for a single organization to have an out and out monopoly on it. They call it rare in the series as well, so who are we to disagree?
Back once more to it being one of those things we just need to accept. Despite there being entire buildings of it, and ships coated in it. Because else it is something any relevant power can gather in sufficient quantity.

I just figured the void century was the government erasing the horrible truth about how they came to power and what terrifying crimes they committed to get there. Basically, they erased the entire change over of government from history just to keep the moral high ground and not be looked at for the terrifying monsters they are. Alternatively it could be the use of the "ancient weapons" that wiped out most of civilization, leaving them to pick up the pieces and they cant risk knowledge that deadly getting out ever again. Like, imagine if we had some horrific world wide nuclear war. We dropped bombs big enough and numerous enough to shatter landmasses, erase entire nations, flood the world with massive tsunamis created by flash melted and boiled ice caps. Only a few scattered remnants survived. The world government took over, and ruthlessly suppressed and destroyed all knowledge of these times until all thats left are vague legends on ancient weapons, powerful beyond belief. The entire century no records were kept, or at least, none publicly available, thus creating whats known as the void century.
I am pretty certain that the void century is the WG covering over their crimes as well. And that One Piece is some sort of history book.