Even though I never had a problem with symmetrical sticks (more the loose-ness and closeness of the sticks), "tradition" is a really stupid reason to make a critical design choice. "It simply works the best" should be the only consideration for a game controller.
I honestly don't trust their explanation. They're right now marketing towards a nostalgia feeling of being a part of the Playstation family of consoles for nearly 20 years. Saying "we're sticking to what Playstation owners are familiar with" is just piggy-backing on a current market push.
The truth is that Sony made a TON of prototypes of controllers and had their first party developers (like Sucker Punch) test them all out and provide feedback which is how they eventually arrived at the DS4 design.