Why? It's not that important, but Center with better Handling will have less turnovers...
that could be, but you won't find a center's handling skill reflected in the player rating in the boxscore. ok, I know, you don't have to care about that, but the transfer market will care.
My impression is that player rating is contingent of the number of successes and failures in the different actions that he takes in a game. At least that's how I explain why players generally get lower ratings in TIE games than they get in normal or CT ones. So yes, from this point of view it is always better to have better skills.
As far as handling for centers is concerned, I think there are so few handling checks that having atrocious handling will barely affect the ratings. This is probably due to the fact that since the C is camping under the basket, he barely needs to move to get a good inside shot: it's something along the lines of get the ball and shoot it up. But that's of course just my experience. FWIW, my C with atrocious handling and passing has less than 1 TO per game, despite being a starter for most of the season.
"I don't know half of you half as well as I should like; and I like less than half of you half as well as you deserve."