Not all UN bureaucracies are bad and inefficient. The French invented the metric system, but they no longer control it. A group of societies down at Saclay south of Paris work for the UN, have diplomatic status and do a good job of guaranteeing a single standard of measure for the whole world.
In a case like that, UN administration means allowing a group of technicians to do their work without political interference.
Now, ICANN is a private corporation contracted by the US government to be a name registry. Nobody wants their infrastructure controlled by another country, and particularly one that flaunts international law and uses all means available to punish countries it doesn't like. So sure, I say take the ICANN folks, give them diplomat status, nice CD plates on their cars, put them on the payroll of the UN with the charter to maintain the infrastructure of the internet and leave them alone.
Now, spam is a problem that's gonna need a global solution. It may be that "they'll always find a way around", but the current spam traffic is costing billions of dollars.