To preface, I started mounting my skis at center 10 years ago for the balanced feel. I've learned a lot about this, and it seems some manufacturers still don't understand it.
When symmetrical skis were first introduced, I was always led to believe I needed a directional all mountain ski to get the best all mountain performance. I would then just mount it at center for my preference (and lose a little of that designed performance), but still be on the best possible ski. I would have to lean back on my heels to really get power from my carve, but I thought that was the best I could get.
Symmetrical skis have always been sold as park specific, made for "skiing backwards," and suck for anything powerful on the mountain. I eventually gave some a chance and realized this is completely NOT the case. I was actually able to power through a turn keeping my weight over the balls of my feet like a properly mounted ski. I don't know why they are sold as such park specific skis when I have so much more edge control all over the mountain. It has nothing to do with going backwards.
Symmetrical skis should be marketed as skis for people mounting at center. It has nothing to do with park or skiing backwards. These are negligible compared to the performance gained from being at the center of the turn radius. I was led to believe skiing performance directional skis at center was the right thing to do for a freeskier by manufacturer marketing. But you lose performance skiing forwards, backwards, and everything else. I don't know why any manufacturer would recommend a ski to be mounted at center if the sidecut center is farther back, yet I still see this every year. I know there are some symmetrical skis out there, but there are a majority of freeski skis designed around a center mount with non-centered sidecuts. I don't get it.
TLDR: Being at the sidecut center means everything for actual performance. Why do so many manufacturers continue to make skis and recommend mounting at center if the sidecut radius is farther back? This is a terrible concept.