In 2017 appear.in published some numbers. They saw ~15% were not able to do P2P. https://medium.com/@fippo/what-kind-of-turn-server-is-being-...
Reading your stackoverflow link my guess is that you aren't using STUN. A P2P connection can't be established without a NAT hole punch.
Also if possible I would avoid the terms `Full-cone NAT` and `Symmetric NAT` they don't do a good job of describing what is actually happening. NAT Mapping/NAT Filtering is the best way to describe it. I wrote a little bit about it here [0]. To see what type of NAT you have try stun-nat-behaviour[1]
[0] https://webrtcforthecurious.com/docs/03-connecting/#nat-mapp...
[1] https://github.com/pion/stun/tree/master/cmd/stun-nat-behavi...