I think it's both.
One Gemara says: "if the Torah requires you to thank Hashem after you've eaten, then by logic you're certainly obligated to do so beforehand." (Thanking afterwards is certainly a mitzva not a matir, so presumably by that logic so is blessing beforehand.)
Elsewhere (reisha d'perek keitzad mevarkhin) we find: "whoever benefits from this world without a bracha is stealing from G-d"; or "Scripture says to G-d's are the earth and everything within it; but it also says the heavens belong to G-d but the world was given to humanity, so which is it? The former before making a bracha, the latter afterwards."
But to really make things interesting, here are two more points to consider:
There's one place where Rashi talks about stealing "the bracha", not the food. This is explained as talking about a case where you just say a shehakol on everything, rather than properly identifying and articulating the right bracha. Hey you said some kind of thanks so you're not "stealing the food from G-d", but you really should be saying the right bracha. (So if you will, you could call this the matir has been satisfied but not the mitzva.)
An onen (someone caught up in the burial plans of an immediate relative) is told to be passive and not perform any "yes-do" mitzvahs other than the burial. An onen does not recite brachos before eating (I've heard several mourners describing that first moment of eating without a bracha, when it sets in just how much their world has changed.) Presumably whatever matir component is lifted too?