That isn't necessarily incompatible with alternate domain name systems. If OpenNIC is registering names under .pirate and ICANN is aware of this then it can simply refrain from using .pirate as a TLD and you still have a unified namespace. It just happens by consensus rather than central authority.
If they would get along a little better then you might even have the ICANN root servers direct queries for those TLDs to the OpenNIC servers. It's not obvious what benefit is achieved by not doing this.
If they would get along a little better then you might even have the ICANN root servers direct queries for those TLDs to the OpenNIC servers. It's not obvious what benefit is achieved by not doing this.