Having said that, I don't personally believe Arthas is that good a comparison here. The soldiers following him to Northrend wanted vengeance too, just not as fiercely, and first and foremost they were following their prince's orders; once the ambassador informed them the king orders them to return, they obliged, which is why Arthas burned the ships. Muradin was on a quest of his own and felt tagging along with Arthas would benefit them both, being friends and all; he didn't know about the changes Arthas was going through till it was too late. When Arthas turned Scourge, no Alliance-alligned human, elf or dwarf followed him anymore.
Alliance is not pure, there are atrocities in its list of sins. Nobody can argue the Horde is pure either, but there are good reasons why it became this way.
- For Garrosh it began with wanting to procure better living conditions for his people, then as time went by his focus shifted more on Horde Supremacy, and Cataclysm hammered the last nail in ruining Durotar into an even worse mess then it was and Twilight Hammer played the most pressing part in sparking the war.
- Orcs followed Garrosh, because the majority of them had been born and raised in internment camps and nowadays lived in a shitty piece of land that Cataclysm made even worse. They weren't satisfied in their lot in life, while their neighbors, the night elves, lived in lush forests.
- Thrall didn't care to take the job AND he became busy with important world-mending shaman-stuff, so he chose Garrosh, who would certainly be able to bear the weight of war and leading their people through tough times one way or another. Tbh, at that point Garrosh could still have become a better orc, as the Stonetalon quest and overall disgust at backhanded tactics showed.
- Other races followed Garrosh's will, for at first there was no serious beefs with him, only minor ones, then as those beefs grew the most pressing reason for staying in the Horde became fear of retaliation; the orcs always outnumbered the other races and there was no certainty the other non-orc races would pick your side should you rebel. Now that shit is really hitting the fan they're finally ascertaining their position and making moves against Garrosh.
I believe the bulk, if not all, of the orcs will turn against Garrosh too. Orcs & Humans is the persistent theme of Warcraft, so it wouldn't work if we annihilated most of our core-race. I think after the fall of the Thunder King the remaining mogu will see benefit in following Garrosh and the rest of his forces would be Blackrock orcs. Villain-races for the endboss instead of our brothers.