If APIs can be copyrighted, it would seriously harm interoperability. For example, if the ruling holds, someone could make a payments service which replaces Paypal so seamlessly that to integrate it you can just change the 'paypal.com' string for 'competitorsbrand.com' without redoing all the work you did for Paypal integration. This would be bad for Paypal but would be great for making the market far more efficient. Similarly, if it is reversed on appeal, Wine and Mono could be considered copyright violations and sued by Microsoft.

If it extended to non-software interfaces a reversal could be even worse - imagine if the idea that turning the round wheel in front of the driver causes a car to move in the corresponding direction was a copyrighted interface? In that particular case, Copyright in the US wouldn't have expired until 1985, so other manufacturers would have needed to come up with different interfaces, and switching makes would have been hard.