When a player has played a long time in one city and becomes the face of an organization, it's really hard to see him play someplace else. Tony Gwynn just belonged in a Padres uniform. Biggio belonged in Houston. Jeter belongs in New York. Sometimes it doesn't make fiscal or even competitive sense. But it's still great for the fans. In Paul Konerko's case, the fiscal case doesn't make sense, but at least for a year or two, the competitive decision makes sense for the White Sox.
Konerko is a hard player to figure out. He's hit over .304 one year and then .234 the next. He batted .312 in 2010 after batting .240 just two years ago. But all things considered, other than 2003, Konerko always finishes well above league average in OPS+. He takes his share of walks. usually slugs near .500 or above and according to White Sox fans, plays his position well (though that fact isn't supported by fielding metrics).
The signing also means that Konerko and Dunn can do some damage to AL teams in tandem. If Konerko had left, then you were basically replacing his production with Dunn's leaving the White Sox no better than last year. But the two in tandem gives the White Sox, with their pitching and bullpen, an excellent shot at the AL Central title since the Twins have no improved significantly and need to sign Pavano just to be as good as last year. The Tigers have improved, but don't appear to be significantly better or worse than the White Sox or Twins. Konerko's signing makes a great deal of difference in this division and thus is probably worth the cost to the White Sox.
We won't get into the material costs of signing Konerko. They probably will not work out in the White Sox favor any more than Jeter's contract will be worth the money the Yankees paid. But in this world of free agents, team hopping and instability, it's nice to have one face of a franchise (or two or three) stay in one place for his career.