It's part of the lex orandi/lex credendi thing. How we worship God (or don't as the case may be) is important. I can barely remember the sign of peace it's been so long since I attended a New Mass but I do remember it being very jarring and disorienting.
Two of the churches I attend have an extremely laid back sign of the peace. Folks barely turn around. Most just nod. The latter is my favorite.
The third one had a couple of VERY enthusiastic peace signers. My option there is to stare straight ahead and shake hands if pressed.
I'm old and it's not easy to jar and disorient me anymore. There aren't many perks to being old so I hold on to the few that are offered...and am very grateful.
I understood that the Sign of Peace was optional and have been to a NO Mass where it was omitted.