There is no reason why you can't host something behind CGNAT: you just have to use NAT-PMP or PCP to allocate a public exterior port. The issue is then whether

There is no reason why you can't host something behind CGNAT: you just have to use NAT-PMP or PCP to allocate a public exterior port. The issue is then whether anyone on either side supports that... but it isn't really NAT's issue.