Earlier quoted context omitted.
The idea of those who favor "kings and aristocracy" is more that we'll always have people around with more power than others (elites), and that formal transparency about who these people are ultimately improves accountability. Would you work for a faux "anarcho-tyrannyist" firm where you have no idea who the CEO is and who the managers are that can fire you or cut your salary?
That, of course, is ultimately extremely defeatist compared to the ideals that the USA claims (the practice and history, on the other hand, would be another discussion). One of the things the right wing (especially the religious right) in the US does far better than any other groups is to claim lofty egalitarian or noble-minded principals while not applying them to themselves. But if we throw that out, and want to em…
Making it less likely that companies become very large, profitable and valuable discourages investment in companies of all sizes, by reducing returns on small cap and venture capital investing.
As for direct effectd, "taxing the shit out of" the rich, as you suggest, would impact far more than large incumbents. It would reduce the incentive for the rich to invest in general, by reducing the size of the reward for becoming very wealthy, encourage capital flight and expatriation of the highly ambitious and capable, and reduce the after-tax income of the best investors, and with it, the volume of new investment.