Okay, so let me expand on why I see Karkat as such a wild card. It's not his leadership, I'll just say that outright. Even when he was supposedly "the leader", most of the tactical, long game decisions were done by Vriska, Terezi, and Aradia than Karkat. It's his Social Influencing. And it could very likely match, if not surpass, Steven's. Here are his feats:
Got a group of 11 trolls who hated each other to work together well enough to defeat The Black Kingdom of Derse, a feat that has a very low success rate across the multiverse. (The Black Kingdom of Derse always, 100% of the time, manages to conquer its home universe and very few attempts to beat them succeed. I know I said that his leadership isn't a factor and I fully concede that it was mostly the tactical efforts of Vriska and the others I mentioned above that they managed to succeed at all. The main point is the wouldn't have even been able to tolerate each other well enough to make any of those plans uf it wasn't for Karkat. These people hated each other on a very deep level, with few exceptions. I'm talking about "this person is personally responsible for some of the most traumatic events in my life. The horrible things they have done have physically and emotionally scarred me and shaped me as a person on a fundamental level. I'd love nothing more than to kill them horribly." Levels of hate. Karkat managed to unite them against a common enemy, kerp them from killing each other, and managed to get them to tolerate each other for years despite this. That feat alone is arguably just as good as anything Steven has done.
Karkat's friendship with Eridan. Eridan, at the start, is a genocidal maniac who kills kids parents for a living. He hates landwelling trolls and has virtually no reason to put up with them once Feferi dumps him and stops acting as his morality leesh. Karkat is a landweller who keeps his blood color secret (showing blatant disrespect for the social structure the Eridan believes in in the process). Yet, the two get along well enough for Eridan to come to him for romantic advice and ultimately spares him once he decides to betray the team.
Managed to calm Gamzee down in the middle of a religious crisis induced rampage.
Is prophesied to be the one who will guide trollkind to a new era after its near extinction.
Befriended Spades Slick, Derses' spymaster, in their first encounter and convinced him to turn his back on the Kingdom.
And finally, his Aspect is Blood. Meaning, that if he'd gine God-Tier, he'd be a God of Blood. To put that into focus, if he'd chosen to become a God, he would've been a God of Teamwork, Friendship, and Social Connections.
Why do I bring this up? Because Homeworld historically has a problem against Social Influencing. Lapis Lazuli, Peridot, Bismuth, The Cluster, Rose's entire rebellion. Homeworld's dehumanizing nature would provide the perfect window for Karkat to talk them over to his side. Not only would his more savy friends notice and likely advise him on this exact thing, Karkat himself would have good reason to in-character. Karkat, under his loud abd crass exterior, is a reasonable and empathetic person. He'd most certainly sympathize with the harsh conditions most gems live under, especially in regards to fusion. Karkat is a huge romance fanatic, and once he understood fusion, he'd be disgusted with how Homeworld regards it. Basically, once Karkat steps up to the plate, Homeworld could likely find itself dealing with another rebellion on top of the war they're already fighting. Plus, Karkat's physically 6-C, so only the strongest gems would be able to shut him up once he started talking.
The flipside is, this would only come into play once Homeworld reached Alternia proper, so it'll already be a good ways into the war. Karkat's a kid, he's not gonna be in space where all the fighting is happening.