Sure, rules can be taylored to a playstyle and favor one over the others. But who says one should always use the best-suited tool?Most of RPG actions take place outside the rules, anyway, especially with CaT. When the paladin has a choice between breaking is oath or killing his father, what rules are there to guide him? That's pure theatrics. The rules will just tell you the outcome (maybe that's the father who will kill his daughter after all). The drama is all yours and ripe for the taking. You just have to build the situations for it to flourish. (Prewritten characters are my secret sauce, there.)
And I'd argue 5e is quite fine as a CaT engine, as multiple APs showed us, even though one can of course get better suited tools, tools explicitly made for CaT. But you can make good races with ordinary cars, the existence of sport cars doesn't prevent this. 5e gives you flashy powers and times to shine (not a given in CoC), it ensures evevery character will be able to add something to a fight (again, not a given in many RPGs, think Shadowrun for instance), and of course it gives you the basic architecture needed: just tell me what you do, and we'll make it work (or spectacularly fail), with combat powers, skill checks, or saving throws.
Even a tool like CR, that one might put firmly in the CaS spot, can be useful for CaT. You just use it differently: to convey the good signals when, for instance, you're just playing an official campaign (so no CR calculations) and want to help the players acting along the disparity of power on display. Or you can use it to build encounters at the most suited and needed level of tension for such and such scene, rather than as a guide on "how to completly deplete PC's ressource in a day". Maybe the paladin's father is especially weak, making it all the most tempting to exert your power and become a faithful paricide, who knows?
I play in a lot of games and am not DnD-centric at all, but my DnD games are CaT all the way. That's just the way we play it, without adding anything, and playing more or less RAW.