Capital seems to work well in Switzerland too, where there is no opportunity for a king-like figure to arise.

Capital wants clear and stable rules. If a king can provide those, then Capital likes the king. I'm not sure clarity and stability of rules is a property of the upcoming american monarchy.

Any statement like 'Capital wants' is foolish. Because by nature there is competition, and very few things beyond the basics are good for all capital.

And if anything history often shows that capital doesn't want a king while the people demand it.

Capital, in an existing capitalist system, never wants an actual (as opposed to a distracting but powerless figurehead, which they might want) king-like figure (because such a figure is a transfer of power from capital as the existing ruling class to the monarch-like leader), but it is also structurally vulnerable to the emergence of such figures because for each individual capitalist there is an incentive to cooperate with any emerging king-like figure to receive favorable treatment over other capitalists.

This is one of the areas where a popular leftist mantra tends to be right in its conclusion (“Capital will always side with fascism”)—and this works for a wide variety of authoritarianisms that don’t overtly seek the utter destruction of private capital, not just fascism in the narrow sense—but exactly backwards in its rationale (“because fascism does not threaten capital”, when in fact the reason is because fascism does threaten capital, but does so both less and less immediately for capital that cooperates with it than capital that resists.)