Actually, the Byzantines did many of these things! Several Byzantine dynasties enjoyed (relatively) long periods of (relatively) stable succession, and at least attempted to keep the title of emperor from passing out of the family. The idea that Byzantium is naught but intrigue and assassinations is basically the fault of the 18th-century historian Edward Gibbon - but that's not exactly what you were asking.

You already pointed out the Isaurians (717-802), but the Macedonians (867-1056!), Komnenoi (1081-1185), and Palaiologoi (1261-1453 - especially impressive considering everything else happening at that period) were nothing to sneeze at, either. The Byzantines certainly took steps to ensure legitimate succession, even despite heaps of court intrigue: nominating younger brothers or sons as co-emperors (like Leo VI and Alexander/Constantine VII), or setting up/hoping for trusty courtiers to protect underage heirs (like Basil Lekapenos for Basil II and Constantine VIII during the regencies of Nikephoros II Phokas and John I Tzimiskes). Some Byzantine historians also do link imperial rank to bloodline: Michael Psellos (Chronographia 2.10, 4.1-2, 6.11-4) and Michael Attaleiates (History 5.1) both seem to think emperors like Romanos III, Michael IV, and Constantine IX acquired the right to rule only by marriage to Zoe Porphyrogenita (the daughter of Constantine VIII). Yes, Byzantium had its share of dramatic reversals in power - especially during Iconoclasm, or after the Fourth Crusade - but even despite wildly unpopular emperors like Michael V or Michael VI, or even dynasties like the Angeloi (five emperors 1185-1204), the empire as a whole was remarkably stable. In any event, I think it's a bit unrealistic to expect all 1000 or so years of even a very powerful empire's history to fit under only a few dynasties - and from what I know of western medieval history I don't think Byzantium compares terribly with the monarchies of, say, England or France.