I never heard of OpenNIC before! Cool project. I wonder how complicated would it be for a layperson like me to have my website work on OpenNIC and regular DNS at the same time
Not sure it's possible because dotCom is owned by verisign and designated to the internet root servers. Your ISP, ISP Peering DNS, and any other DNS service would override any of your DNS zones.
It does make me wonder if I hosted my own root servers for a new dotCom tld would I get chased down by the internet police?
No, there's no internet police who would stop you from doing that. However you had better point your .com to Verisign's .com or so many things won't work when connected to your DNS server. Also you will never get IANA to recognise you as the new authority for .com which means people will need to go out of their way to use your root zone instead of the de-facto-standard one published by IANA.
It's a bit like signing your website certificate with your own root certificate. The protocol itself is agnostic to who issues the root certificates, but good luck convincing distros to install yours by default, so your website will only be accessible by people who go far out of their way to install it.
It's a shame, because ICANN being under US jurisdiction is effectively an attack against the DNS.