I replied to the Sox fan survey a few weeks ago and commented on the scoreboard. The video screen's size isn't as important to me as what's on the whole surface. It's a scoreboard, but there's no score on it.
I suppose the entire centerfield board could be covered with a video screen, since the technology exists now. The only limit is the cost, but isn't that what sponsors are for? In Bill Veeck's book, "Veeck As In Wreck," he told the story of the construction of the original monster board in 1960. It cost over $300,000 to build, but the cost was borne entirely by the sign company who recouped their money from ad revenue in a few years.
To me, the board should carry the line score, the ball/strike/out count, and basic stats (hitter's BA, pitcher's ERA, etc.). Everything beyond that is gravy. That leaves plenty of room for ads, replays, novelties, trivia, and whatever else they choose to display.
And this is the home of the White Sox -- the place where home-run celebrations began as over-the-top eruptions of goofiness. In the design of the 1960 board, Veeck was inspired by a pinball machine in Saroyan's play, "The Time of Your Life," that exploded in celebration of a jackpot score. Fireworks, of course, but also Roman candles spitting out the top, lights that chased and flashed in random patterns, smoke, sound effects (dive bombers, Hallelujah Chorus, etc.), strobes, and occasional surprises like "TILT!" signs. The USCF board has the fireworks and lovely chase lights, but it could use more personality and unpredictability.
A full-size video board could give them more options for that, in addition to the lights and the fireworks. And as a side benefit it could actually be a board that shows the score.