Earlier quoted context omitted.
While you are correct that LOC is not a full measure of productivity, and there are many factors to consider, it would be nonsense to say that merging code has no bearing on productivity. All things equal (and disregarding engineers whose job isn’t coding per se), submitted code is the essential deliverable of a software engineer.
No, “solved problems” is the essential deliverable of a software engineer, and the more senior one gets the less often “submitting code” is the correct path to solving a problem. Someone might submit code based on your work, but there’s no direct correlation between “submitted code” and “did your job” at higher levels.
Sometimes a great engineer spends a month tracking down a 3-line fix, and that’s just what happens with complex software. But by and large, if an engineer averages only a few LOC a month (and I’ve unfortunately seen this way too many times) then we probably have a problem on our hands.