Yeah, he's got all of the additional skills needed to be good on grass, but he's missing a couple of fundamental things.
1) A weapon (even minor weapons suffice [see Hewitt and Murray])
2) A mentality along the lines of 'I'm backing myself to hold serve 6 times in this set'. I don't think Fognini has this, and every time he steps on court, he knows he will give away his serve a few times, regardless of the surface
The first is obviously most important, but I really think number two is key as well. If you look at all the players who excel on grass, most of them (even those without 'big' serves) can stay concentrated for an entire set. Obviously breaks will happen occasionally, but the principle on grass is to make sure the opponent has to play some great points in order to do so. So-called 'clowns' like Fognini and Gulbis will never be good grass-counters, because they themselves have a very realistic chance of playing themselves out of sets before they really get going.
Malisse might be the exception to this, but later in his career when he became a more consistent threat on grass, he tightened up his mental approach to the game.
It's also worth bearing in mind that this all applies less to Wimbledon courts. There's no reason why Fognini can't do well on those slow courts, but the same problem will arise as on other surfaces. He will lose to the first great player he encounters because he has nothing to hurt them with.