It's their right because we've decided as a society that it's often useful for people to have that right. There's no physical reason that knockoff publishers couldn't have printed dirt-cheap paper copies of Harry Potter as the books came out, but I think things ended up better without them being allowed to do that.
> How is it their right to push back the expiration date on their copyrights ... [and] to abuse DMCA takedown
These are a completely separate issue, and are less so "rights" than "practices which powerful players do and sometimes get away with".