We don't know that actually. Go back to what Borek said and read it with a modicum of suspicion rather than a desire to dispel those suspicions:
He smiles bleakly. "Karag Dum remembers much that others have forgotten, even when some might prefer we didn't. Even when we might prefer we didn't."
The above looks like Dun was getting something for its power and keeping the deal secret because the High King did not want to pay other holds for their magic, hence, even when some might prefer we didn't
The High king in this situation would prefer Dun did not know about their resources so they too could be ripped off.
Eh, he might have been talking about other secrets, non-Waystone secrets, actually.
But, instead of a cynical everybody-out-for-themselves perspective on things, have a depressive one instead; Thorgrim might not want them to know because... he doesn't want a ton of people to know that the Runes of Valaya are running out of power and will fail and the Dwarfs are totally and irretrievably doomed. Because if a ton of people know that, then things can get a bit risky and explosive or there is potential for huge upsets and panics amongst the whole of the Karaz Ankor. So yes, Thorgrim might not want most people to know how the Dwarfs are inevitably doomed. Heck.
Thorgrim does not to know how the Dwarfs are inevitably doomed! He'd rather not have known this either, and understood as soon as he sat the throne, why his uncle allowed himself to be carried away by his wounds.
Although, when it came to "other people" my mind had actually wondered about the other Holds and the Runelords. Namely that, Karag Dum knew why Karag Dum and the Waystones were important and key to the defense against Chaos.
Despite how the other Runelords of the Karaz Ankor might not have wanted them to know why they were just oh-so-important to the Karaz Ankor.
The Runelords that spoke bitterly at the conclave, and the people that started the cultural shift against Karag Dum (because it wouldn't just be Runelords alone), would rather that Karag Dum be known for suspicion and "How do we know they're worth their word anyway, eh?" Because to admit otherwise, is to admit that they failed to prevent the end of the Silver Age.
But if Borek knows the truth, if Karag Dum knows the truth... Despite what all the people of the Karaz Ankor who have been accusing Karag Dum might want... ... Well.
So, if anything, this is probably a Karaz Ankor-wide politics thing. Rather than a Karag Dum-High King Thorgrim matter.
Though technically, I guess High King Thorgrim would
also prefer Karag Dum to not march up to the rest of the Karaz Ankor and go "'What good are we', eh? 'Untrustworthy', eh? What does Dum do that is so crucial and important?
Well let me tell you, Beardling...!" And cause tons and tons of explosive friction in the Cult of Thungni and possibly sour the relationship the Runesmiths have with their home Holds; because if
they were the driving part for casting rocks at Karag Dum, and
they misled the Dwarfholds from not sending enough backup to rescue Karak Vlag and Karag Dum, then... ... Yeah.
I think Thorgrim, if he has feelings on this matter, is probably something similar to that of Thorek's reaction and bitterness/worry/concern upon learning about the rifts between Karaz Ankor and Karag Dum Runesmiths: namely that of "Shit, this could cause a
huge political rift and cause tons of people to go Slayer, and cause so many Grudges..."
Thorgrim isn't worried about people worrying about Karaz-a-Karak stealing energy. That's not a likely worry, and the Throne of Power is meant to power the Protections of Valaya and other Great Works. It's all utility and defense and function and so on. No, Thorgrim is worrying about the same sort of thing as Thorek is.
And it's far more likely and plausible -- in some kind of bad-case-scenario or even just a not-perfectly-diplomatically-smoothed-over-scenario -- that Karag Dum and Thorek finding out the truth of things, could cause a ton of political upheaval, concerning the anti-Dum feelings and accusations that were thrown around.
Karak Vlag returning and Karag Dum being recovered, could be a shot of enthusiasm and hope for the Dwarf people. But it might also be the potential for a huge political headache.
Thorgrim will probably be more relieved at the Dwarfs having a future now, but also with new issues to worry about, too.
If we could somehow get Borek, Thorek, Belegar, and Karak Vlag, and Karag Dum, to somehow come together and...
not cause a ton of diplomatic fallout from things? That would be great.