This is really the distinction between the mentality of a technical manager and an individual contributor.

Managers never got to write and internalize every line of code anyway. Arguably their essential skill is producing useful stuff without needing to do so. So is that 'cognitive debt'? When I use an agent to code, I do the same things: I validate the direction, organization, and core decisions, but delegate the details. It's an intentional calculation of risk, managing the scope of future problems if there's a failure of implementation somewhere.

It's a question of where you put the value of cognitive focus. I don't understand 'line by line' how my car's ICE works, even though it will likely impact me at some point, because while I might be able to fix it myself if it breaks, the likely applied solution will be to delegate that work anyway.