You've touched on the hidden crack in otherwise solid balance-of-power theory: the balance gets deformed when a single ruling class assumes leadership of substantially all the organs of government.
Balance-of-power only works in systems with several groups of elites, groups composed of members who wouldn't be caught dead crossing over into another group. The United States used to have this pluralism of elites, but cultural and war-fueled centralization wrecked this plurality. It's now a "revolving door" system wherein a single group of elites - a ruling class - has assumed leadership over all organs of government.
To see what I'm saying, imagine an alternate U.S. where matriculating at Harvard gives you the shoo-in as a federal politician but kills your chances at becoming a state-level politician, even Governor. If you matriculate at Yale, you have a leg-up for a judgeship but ruin your chance at becoming a politician. And so on...
It's this kind of social fabric that gives you a pluralism of elites.
Interestingly, I had never considered a system that way, I had analyzed ways to divide power and keep different groups of people in them. As for example, that a political party that participates in elections to the parliament, can not do it for those of the presidency. In the same way the politicians, that is, a senator could never be a president, and a mayor or a governor, could never be a congressman, that is, maintain the separation of people who exercise a function or another. However, there is the problem of the influence of money, when people finance politicians to have power over them. However, I like your system a lot, I'll think about it.