Earlier quoted context omitted.
Why a new agency? This is already very much within the FBI’s jurisdiction. Why is the international surveillance of U.S. journalists and their sources not visibly a priority? In my opinion it’s a matter of policy. This comes from the top down. Bringing justice to international actors opposing democratic ethics is regrettably less of a priority today than enforcing highly publicized and politicized criminal cases.
IIRC, within the FBI’s jurisdiction and international don't go together. Isn't the FBI restricted to operating nationally only? But to answer your question more fully, you can't solve this problem without supranational cooperation. A "police force" working to safeguard the Internet would have to work under authority of the UN, not any single nation.
It's an association of governments, where they get together and organize things. All the power is in the individual governments. There are some grey areas and exceptions, but overwhelmingly the above is the case.
The UN could coordinate cybercrime law and national agencies.