Grabo's playstyle is pretty different from Olli Jokinen, but generally you want a more selfish guy as your 2C, for multiple reasons. A super unselfish center is more heavily reliant on his wingers being good scorers... and not many teams have those on the 2nd line. So you have one of their major talents being largely wasted on elevating tweeners. Grabo works well with guys who may not have all-world finishing ability but who can work the boards well and defer to him - this is much easier to find in typical 2nd line wingers like Glencross, Umberger, Kulemin, etc. A side benefit of that setup is that you also get an effective two-way/shutdown line because those guys tend to play aggressive close contact disruptive hockey. There is yet another benefit - a go-to C is also automatically more involved in the play physically (either through throwing around his bodyweight or positioning-stickchecking). Playmakers need space so they can make fancy plays and as a result need more separation. That's why so many of them seem like they float so much. Here are some "me first" style centers to various extents - Jeff Carter, Ryan Kesler, Jordan Staal, David Legwand, David Backes, Mike Fisher, Brandon Dubinsky. Also Plekanec, Bergeron and Seguin to a smaller extent. Note any similarities (minus Seguin)?
At any rate Grabo was able to be a very effective even strength player with secondary guys accompanying him.