AFAIK, Heydrich was an extreme hard-ass, but I don't think he was INSANE like most of the Nazi higher-ups.
Oh, he was certainly insane. Just not in an apparent, rabid-angry dog kind of way. Rather than a pathological hatred of any particular group, he had a pathological inability to have any concern for anyone other than himself, and sometimes not even then. He had the hallmarks of a sociopath: lack of empathy, manipulation, narcissism, and boldness. He had, at times, a lack of regard for his own safety (see his time as a pilot in the Eastern Front, or his attempts to fight his own assailants).
This makes him the worst possible choice, in more ways than one. His lack of ideological adherence to Nazism, but his adept ability to feign it to the extreme, means he's likely to effectively and efficiently apply complete brutality and unfeeling mechanisation to the Nazi genocides. Moreso than were applied IOTL. Add to that the sociopathic need for control, and you'll see something like the East German Stasi but across
all of Europe.
But the second thing is, what happens if he's leader of Germany when it wins and becomes a superpower? Opposing perhaps America or a rump USSR or Japan or China in a Cold War scenario? He's not going to quietly coexist with them. He's reckless and self-absorbed and believes he is the best at everything, like any sociopath. He'll drive postwar Germany towards brinkmanship and beyond, and likely start a nuclear war (assuming Germany obtains nuclear weapons, which is probably the only way it'd win the war anyway). And
he wouldn't care.