Well, Dreamweb is pretty close to this; you actually can pick up almost anything you see and try to use it in some way, and most of it is stuff like cheese and toothbrushes that serve no use. And specific items are still required to progress, and even better, sometimes it will tell you why the butter knife won't work but the other type of knife will. (That's a very rough and vague example)
The only issue being is that the game doesn't really make the most of this setup, in fact, that could sum up a lot of Dreamweb come to think of it, which is probably because it was mostly made by three people.
But this is me speaking as someone who's never played it; I've only seen a Long Play of it by Yahtzee Croshaw and his friend Gabe Morton where most of the time they were basically pointing and laughing at the most ridiculous aspects of it (which there's plenty), and also Pushing Up Roses's video which was basically completely glowing about the game and never mentioned the stuff Yahtzee pointed and laughed at.
It was quite the contrast. But then again, PUR played the "talkie" version so maybe that helps.
And I don't even really have a good excuse not to play it, all versions of the game became freeware and regardless of anything, I think it's a pretty fascinating piece of artwork and I've been wanting to record a good-quality version of the PC soundtrack at least, because I do like that music.