PCSX2 is relying on OS API's for controller support, and you know Sony. They go out of their way to make things hard for PC users. :) Simply put, you need a driver.
There are community drivers for dual shock 3 and 4 pads:
I can't vouch for any of these. I've always used non Sony controllers for PC so have no experience with these.
For the widest platform support now and in the future. It'll make it possible to port the game to homebrewed consoles, mobile phones, web browsers, future PC architectures and Linux. Something similar to openmw. This way, the game can remain preserved in the most robust manner possible and enjoyed for decades and decades into the future.