I think cats
should be licensed so if a cat gets out accidentally, it's more easily identifiable and is reunited with its owner more quickly. It would also encourage owners to spay and neuter their cats if the fee for licensing is dependent upon reproductive status.
But I don't think it will help the problem. People who have outside cats will either not license them or leave the tags off them and things will continue as they have. Wildlife would still be at risk from the cats that will remain outdoors. Licensing did not eliminate the dog overpopulation problem, and I doubt it would for cats.
If the licensing fees are directed back into the animal control system for either facilities or education, though, there could be a very large benefit in the long run...