Actually, you CAN have the sport button affect your power, if you have forced induction. I'm about to go down this route. Look at the Active Autowerke Prima Plus.
What I intend to do is run a 9-10 psi pulley with my non-intercooled setup and water/meth injection. In normal, non-sport mode, the WMI is deactivated, and an electronic bypass opens to dump boost once it reaches 6 psi. With the sport button pressed, WMI is activated and the bypass is closed so I reach the full 10 psi of boost. If there is a problem with the WMI, the bypass will open to dump boost. I plan to add a second failsafe/bypass via an AEM Failsafe Wideband that monitors AFR. It's not really necessary, but I have it sitting here collecting dust, so I might as well use it.
These are all mechanical systems using the sport button a sort of a relay to tell them to activate. I don't know that it's possible to have the sport button change the actual tuning of the car with respect to spark advance and fuel trims.