Is it worth contacting the genuine owner of a domain name linked to in a phishing email?

If the email and phishing site is pretending to be from your bank then you can email your bank and report the attack and they will take the steps to take it down.

or

you can take a screen shot of the website and upload it to phishtank.com and the proper authorities (like me) will take it down

or

if you want you can go to websites like robtex.com, domaintools.com, marcaria.com, whois.com or others and obtain the information for the isp, registrar, webhost or get the contact info from the website itself and contact all of them directly and report the phishing abuse. But the report would be taken more seriously and actually followed through if the companies were issued a proper cease and desist letter from the companies in charge of taking them down.

To answer your question:

Those in charge of the site have access to the content to remove the phishing attack. So yes it would be worth it.

With the rest of what you said china and such. It depends what kind of attack it is. If it is just a hijacked website then the file is embedded within the other files of the site itself. For example looking at the website files you'd see; images, page 1, page 2, page 3, main page, sounds, phishing page. The fraudsters just like to hide it amongst them. If it's a hijacked website the website owner, registrar, isp or webhost can take action.

But if it's a hijacked server then the source of the page is the server itself and therefore only the company responsible for the server has the authority to shut it down. The website it happens to fall on is just a victim.

If it's a commercial hosting (the fraudster put up their own website, didn't just hack a preexisting one) then you would contact the registrar, isp and webhost. No sense in contacting the owner of the website as that is the fraudster.

If it's a free hosting site then you contact the free hosting company. No need to contact the isp or registrar.