I would argue that HL2 was just “Gary’s Mod the Single-Player Campaign”—probably with Valve first thinking more along the lines of something that would look like Gary’s Mod itself if they had delivered it in that state; and then losing confidence, thinking that a pure sandbox title couldn’t possibly be something people would pay for (those really weren’t a thing back then, until GMod itself showed the demand!) So they backed off and built a single-player campaign instead.

But I think their goal with HL2 wasn’t really to deliver a compelling narrative, any more than the point of a modern Mario title is to give a compelling narrative. It’s a sandbox with a goal condition. (Sort of like Scribblenauts, now that I think of it.)