I will take the opportunity to recommend three books (all of which I've already recommended in other threads) that may help clarify the thinking and conceptual vocabulary here.
With respect to "rigidity of hierarchy," our current social hierarchies aren't straightforwardly "rigid" after the manner of a caste-based or aristocratic society, or even of a republican military organization. A better term might be "uniformity." Of course you're correct to identify an elite class and outlook in our society, with its own kind of intransigence and an enormous level of power, but describing it as a rigid hierarchy will rightly earn you funny looks, not only because we have all been trained to regard our social system as at least somewhat meritocratic, but because "social mobility" is in fact incomparably greater in our society than in say a caste system, which is truly rigid. Without the understanding that social mobility in this system is relatively high you cannot grasp the essential flaws of the system. Social
mobility means social
transience, social
rootlessness, and so the elite, being individually effervescent, feels no supra-personal bonds of gratitude or duty to the culture and people. And while an individual such as Bill Clinton, the son of a traveling salesman, can rise to the presidency and from there establish a rudimentary kind of political dynasty, or one like Zuckerberg can rise from an unpopular student entrepreneur to a billionaire technocratic overlord by age 30 (albeit still unpopular

), the system is structured so its mobility exacts not only talent and luck but specific kinds of personality, specific kinds of training and certification, and a high degree of meta-ideological conformity to itself. The "rigidity" resides in the demands imposed by the meritocratic structure rather than in coats of arms and ranks inhered to specific bloodlines. On this subject what I recommend reading is
The Revolt of the Elites by Lasch.
Now with respect to "late stage capitalism" I will echo James in saying this is not the clearest or most useful formulation, but I will disagree with his own substitution, which is perhaps even less clear. The elite are manifestly not capitalists, not in their relationship to the means of production, not in their motives, and not in their small, manipulative, risk- and accountability-evading personalities - and so the system they preside over cannot be called capitalism. Managerialist is the term we want, because it gets not only at the institutional physiognomy of the system but at its very soul - the inner character of the elite class - who are not capitalists, socialists or distributists, but
managers. The means of production are now not typically operated and owned day-to-day by capitalists but by executives, managers, and shareholders (which are often companies run by other executives and managers). Political goals are not truly set by statesmen with any charismatic or traditional authority and with a view to the qualitative good of their people, but by agencies populated by lifer and elite bureaucrats who move smoothly between managerial positions in the private and public sector, convinced of their individual "merit," who pursue quantifiable goods like high rates of consumption. This elite interchangeability creates another distinction between the managerial and capitalist systems, in that it fosters a situation where production is not even necessarily oriented towards profit (profit seeking being a definitive feature of capitalism) since the tightly connected private sector has a practically unlimited trough of public funds and tax benefits to support projects and activities (including propaganda) that are objectively pointless or even operate at a loss. I could go on, but I'll just get to the point: read Burnham's
Managerial Revolution, and then if you find time, Francis's
Leviathan and its Enemies.