The generational succession is VASTLY more predictable than a random one, considering the successor comes from the same house and has literally spent his entire life being groomed and prepared to rule.
It's not unheard of[1]. Ancient Athens used random selection for many offices and some Italian city-states like Venice and Florence incorporated elements of randomness. A lot of historians think that it did help a lot in reigning in corruption and making it harder for foreign powers to influence their politics.
I think randomly selecting a president is probably a bad idea but randomly selecting a parliament and then having them elect a prime minister from within that group would work well.
Whether that's a point for or against depends on whether you think policy thrashing every 4 years is a good idea.