How to use "be more of" in a sentence

I wrote the following sentence as a part of an essay. However, I'm not precisely sure about the usage of "is more of governments responsibility" in the following sentence. Therefore, I would really appreciate it if someone could let me know whether that phrase is grammatical or not.

Some critics conjecture that mitigating this recalcitrant open-ended problem is more of governments' responsibility, while, others, on the contrary, believe that it is governments and giant commercial organisations that could tackle this issue.