I'll let you all keep debating if you see fit. For my two cents...
I don't believe achievements take away gameplay at all. I mean, it's not like I'm trying to get all of the achievements on my first go through the game... Anyway.
I've always viewed HL2 as more of a FPS Puzzler. Not strictly FPS, because, really, what strictly FPS game has you shifting blocks from one side of a wooden board to the other to gain access to a new area.
As for the breaks in activity for "cut scenes" It's to address a problem VALVe calls "Combat fatigue." The same for Puzzle fatigue. They need these scenes to prevent players from "burning out" from repetitive gameplay. ex: Shoot headcrab, solve puzzle. Shoot combine, solve puzzle, shoot antlion, solve puzzle. ect. The talking scenes break it up so it's not simply two or three gameplay types.
That's my two cents.
In other news, I got the "Zombie Chopper," "Keep off the sand," and "Submissive" Achievements since my last post here. Next up, Hack attack, then, the groan-tacular Lambda locator.