If Godaddy is a terrible host and registrar if you are afraid of getting a DMCA notice, then why wouldn't you find a different one if you're that worried about it?
Because such a registrar does not exist. All registrars, ISP's, search engines, and anybody who could possibly be remotely considered a distribution channel for potentially copyrighted material, must abide by the DMCA or risk losing their "safe harbor" status. If they lose safe harbor, they are legally responsible for any and all copyrighted material that is distributed using their services. In other words, if they don't comply with the DMCA, they're fucked.
The DMCA procedure is simple and clear: If you receive a DMCA take-down notice, you immediately cease distribution. In the case of a registrar, that means suspending the DNS hosting for that address. If they don't comply immediately, they're fucked. If they contact the infringing website first, they're fucked. The only option they have is to remove the service as soon as they receive the notice, then contact the website owners and notify them that the service has been suspended due to DMCA infringement. If the website owner replies that their use of the material is legal and they contest the claim, then the registrar (or anybody else) is free to resume the service as usual. At that point it is up to the copyright holder to sue the website owner, and the registrar (or anybody else) is in the clear until a judge tells them to stop service again.
That's how the law is written, and there is nothing GoDaddy, an ISP, Google, or anybody can do about it. It is disgusting, but you have your representatives in Congress to thank for the nasty piece of work that is the DMCA, not GoDaddy.
Point the blame where it belongs and quit letting Congress off the hook for this shit.