They did, it lasted less than a year, and the Nazis didn't ask them to tone down their methods they actively intervened to prevent them overthrowing Antonescu.
A longer lasting, or earlier, Legionary State would certainly be a horrifying prospect. The Iron Guard were truly nut-crackers, even more Cultish than the Fascist norm. Their contribution to the Eastern Front would certainly be different. Hitler moved against them because he wanted a professional Ukrainian army at his back rather than a fanatical mob. Romania would probably be seen in a far worse light, almost as bad as Germany. The Soviets will probably hit down hard on the Romanians when they arrive. This might butterfly the rather rosy view Romanians were allowed to keep of themselves under Communism.