Others have touched upon this, but I'll say it anyways. Silent protagonists work best, I think, in [semi/mostly] non-linear games where you have multiple choices in what to do, and presumably, you're given choices that make some sort of sense but individually appeal to different sorts of people. When you're in a linear game like Half-Life, yes, a lot of your actions are representing what the protagonist is...but at times, especially in Half-Life, some of them aren't, due to the game railroading you in whatever direction it wants to go. This is why I prefer a game like S.T.A.L.K.E.R., where you're given a mission by someone else, and you can choose to do it or completely ignore it - or even sabotage it if you so wish. Sometimes, when you ignore it, you don't do as well as you could've if you'd listened - or flat-out lose - but it makes sense within the game that what happens does happen. Generally speaking, you want to do what the game is telling you to do, because it appears to be the most sensible course of action at the time - but if for whatever reason, it doesn't appeal to you, well, you can also choose to do something else.
There's nothing worse in a game where you're presented a course of action that seems stupid - or something that you just don't want to do for whatever reasons - and you have no choice but to do it anyways. Half-Life (2) is most certainly guilty of this a few times, particularly when dealing with some of the side-characters.
