The Legions are harder to corrupt en-mass. Whether they could have conquered the galaxy is something of an open question though. I mean Ullenor, the Rangdan, etc.
Regardless, the issue was never the Primarchs as a whole or the legions. It was that the Emperor never bothered to create the administrative apparatus needed to secure the Imperium.
I mean yeah, you had Angry-Lad, Emo Priest, BATMAN!, and Cunty Arrogance (Magnus) being allowed to get away with their bullshit but even that is largely because the Emperor just didn't give a fuck.
This is a man who was willing to erase two legions and Primarchs from history, who was willing to purge the Thunderwarriors, and he wasn't willing to purge the XVth once it was seen that the Fleshchange wasn't an isolated incident?
Or who decided to half ass his chastisement of Lorgar. I mean he could have grabbed him by the scruff of his neck and kept him at his side for re-education while parceling out his legion into penny packet forces assigned to actually competent Legions for reeducation and ordering Guilliman to take his legion back through Lorgars conquests and set them to rights. Instead he said "You bad boy Lorgar, I'm gonna burn your toy now. And have a couple of babysitters who are going to let you get away with anything." and left.
The Emperor was either an idiot of the highest order and a raging incompetent who couldn't plot or politic his way out of a wet paper bag, or the purpose(s) of the Legions, Primarches, Great Crusade, Imperial Truth, and even the Imperium as a whole were far different from what anyone short of his own inner circle knew about.