GRE Optional --- is it really?

For non-ivy QF/ FinMath programs such as NC State and UChicago (although still prestigious) say on their website that 'GRE is not required of any applicant'. or 'GRE is optional, however a strong GRE score will increase your chances'. How exactly true is this/ what impact does it give on your chances of admission?

Say a strong applicant with great rec letters, statement of purpose, quant related internship and a near 4.0 gpa. How much will it impact if they do poorly on the GRE and decide to not submit? Standardized test anxiety here...

Appreciate any discussion.
I'm wishing to know above what scores candidate then is better off to submit rather than not to do so???? for gre i'm guessing around 320???