In general as movement, crossing the centerline is not unique to tai-chi, it is the basis for efficient body power and movement. The more you cross the centerline, the more potential you have to work with. You can see how power must be transferred eventually 100% to one side or the other as a form requires. Take speed skating:
http://www1.pictures.gi.zimbio.com/ISU+Speed+Skating+World+Cup+Nagano+Day+1+0q9aucDVODkl.jpg
This is not tai-chi movement per se, but I show this to demonstrate the need to transfer body mass from side to side as a foundational principle. If you skate, the more you engage the core and cross the centerline to 100%, the more power you generate. The same principal can be applied to Tai Chi and the power/energy that results. Or, Net Force=Mass plus acceleration...It's physics.