SCTP can't go through NAT (there is ietf draft in works for that). But SCTP already exist in your favorite browser Chrome, Firefox both use usrsctplib (https://github.com/sctplab/usrsctp) to provide sctp over udp for webrtc signaling.

But there also need to be sctp over udp over dtls (or just sctp over dtls) happen as you can't use TLS with SCTP unordered mode or multihoming.

SCTP slowly gain traction in userspace besides being only in mobile operator networks (lte)