I'm trying hard to follow your argument, but I think there's something missing. If I were to guess, you're making the argument that you can have D&D play that doesn't put those resources in check -- that essentially revolves around resolving conflicts in ways that limited spell slots, or spending hp, doesn't really matter. And, sure, that's true, and I note it above in saying that the resource game isn't always foremost, even round to round.
However, I don't think you can divorce balance in D&D from the resource game. I mean, hp increase and spell slot increase are one of the primary things that improve with level and are countered by similar improvements in foes. Same with the action economy -- you don't get more actions, but you get more efficient and effective in how you can use the actions -- again something mirrored in foe design. A quick test of balance involving the resources in D&D is to go to extremes and see if it hangs together -- can an otherwise level 1 character have inifinite spell slots of any level and remain balanced? I don't thing so. Same goes with a character with 500 hp and regen 500/round. That doesn't balance. Going the other way, can we balance a wizard with 1 spell slot only and ever with a normal wizard? Can we balance a fighter with only ever 1 hitpoint against that same normal wizard? No, because a careful balance of these resources is the core way that D&D balances class design and encounter design. Do you, as GM, have to pay attention to that? Certainly not, but you can't just say that because you don't pay attention to it that the game designers did not or that the game isn't, at base expectations of play, balanced on managing those resources.
I play Blades in the Dark as well, and it's a narrative structured game -- pretty far mechanically from D&D. And, yet, I would say that the balance of how players manage stress is a critical part of that engine. You can't take it out, or introduce a character with overly large or small pools of stress and have it balance at all with the other PCs or the mechanical expectations of the game. And, balance against those mechanical expectations is critically important. To shift back to 5e, I don't see how you can totally ignore the resource management game and still be playing 5e according to the designed expectations. You can play it that way, of course, because 5e is ultimately a GM decides core mechanic, so the GM can decides whatever they want. But, the class writeups, the spell level descriptions, the construction of foes, and the construction of encounters are all very much tied into the expectations of how resource management works in 5e. You can dispense with them, at your table, but that doesn't say much at all about how the game was designed to function, and it's clearly balanced on resource management in a number of ways.