The primogeniture led to failures like “what do you do in the case of a minor?” or “do I divide the empire among my sons (merovingian)?” or “my ancestors all married their cousins, now I, Ivan IV am a schizophrenic!” or “let’s have a utter stalemate each time by mandating utter 100% agreement (Polish Rzeczpospolita”
Only one of your examples is a valid criticism of primogeniture monarchy.
Underage monarchs were a really major problem. The answer, which seldom worked well, was a regent. It only worked when the Regent wasn't after the throne himself and also had sufficient authority and power in his own right to overawe possible opposition. Otherwise, it usually resulted in civil strife or war anyway.
The "divide the empire" problem was the reason behind primogeniture. The empire or kingdom went to the firstborn son, which is the meaning of primogeniture. When he was incompetent and one of his brothers wasn't, he didn't always keep the throne, but that's a different story.
Marrying cousins was also a problem, but the later years of the Spanish Habsburgs are a much better example than Ivan IV. His two grandmothers not only weren't cousins, one was from Serbia and the other from the Byzantine Empire. Dude had a lot of problems, but being inbred wasn't one of them. BTW, historians disagree how mentally ill Ivan was. For a crazy guy he certainly accomplished a lot.
The Polish thing actually makes my point. Rather than a hereditary primogeniture monarchy, they had an elective one. Which meant just about every succession turned into a civil war complete with foreign intervention. Even when he was enthroned, the Polish king didn't have much power.
In fact, the elective monarchy was such a bad idea that when Poland put its reformist constitution of 1791 into effect they replaced it with a hereditary constitutional monarchy, with primogeniture as the rule of succession. The Constitution, of course, was rejected by Polish conservatives and by its greedy neighbors, which led directly to the Second Partition and the abrogation of the Constitution.
The elective veto was, BTW, among the least of Poland's problems. The BIG one was the liberum veto, as you say.