It totally depend of the story and the scene.
Some stories need to show you more than the MC know ; in order to keep the story consistent, or as hint for the player. But it doesn't mean that the whole game have to be in third person because of that.
And a first person POV can perfectly pass to an "over shoulder"-like camera some times, in order to provide a better understanding of the scene. If the MC start to grind against a character ass, or to grope her/him, a pure first person POV would need to either make the MC look to what (s)he's doing, what would be weird, or have use of internal thoughts to explain what is happening. Or you can just slightly move the camera and let the player see it happening.
As for MC's face, personally it don't bother me this much to see it. But being almost 50yo, and also liking to sometimes play as a female MC, I already have to effectively project myself into the MC. What explain that his face not looking at all like mine isn't something that would break my possible immersion ; the MC is already not near to the real me.