The robot killing itself is both a direct action, and results in future inaction, through which humanity may come to harm which the robot could have prevented, had it not killed itself. So that's not a magic-bullet solution.

If it kills itself, it might cause depression in the inventors. So that's definitely not a solution, let alone the only possible one.

A closer solution is to properly simulate humanity and determine which actions work. (There's the ethical question about how good a sim before you've caused consciousness. But I don't think we know enough about consciousness to fully conclude anything there.)

Indeed, in the novels the "inventor" of the 0th law is fatally conflicted upon acting on it.

Do botnets qualify as "robots" and does "harming humanity" include DDoS attacks?

It's the combined plot for pretty much every Asimov book they appear in. That's discussed in the linked video, as well as the grand picture of why they don't really make sense as "laws" since they're basically impossible to define without first defining all of ethics.