While so far efforts at a decent storyline in the gaming industry have mostly met with failure, that doesn't mean that they should stop trying.
It is the storyline that can translate a game's progression into an artwork. Without that, the chance of a game being counted as art is far lower (visual and musical art would still be possible, but that's very restricting).
Why would we deny our medium the ability to extend itself past the amateur, the entertaining, or the immature? That would be a true waste.
Cut scenes, on the other hand, have been proven to be slightly less necessary. If a game can have all the story explained without removing control from the player even once, then maybe it makes sense to remove cut scenes entirely.
Of course, there is a lot more storytelling potential in a scene where the authors have complete control, so cut scenes are an excellent tool if used correctly. It's just that they often feel forced or come in at random times due to budget restrictions and a lack of creative input.
I think the biggest problem with cut scenes at present is that they're mighty inconsistent; you never know if a cut scene is going to happen or if you'll just get a less enthusiastic bit of in-game dialogue. So when it does happen, you feel cheated out of having control of a prominent moment in the game just for the sake of watching some cool action. It's actually a pretty easy problem for designers to solve if they think about it, though; they just need to decide on a logical pattern of cut scenes that fits their game's overall narrative structure to players know when to expect them.
Of course, some cut scenes these days happen in the same engine as the rest of the game and give some control to the player in the form of quick time events, unlike the visually superior FMV. These are really no less divisive in the gaming community than FMVs are, though.
So, yes, you can definitely count me among those many who would miss cut scenes and storylines. I don't think that game developers should rid themselves of any particular design tool except if they feel it is not appropriate to the specific game that they are designing. A blanket policy that restricts such tool use only leads to a production line of similar games, with no variety or diversity in style.