I'm kind of on the same boat- if it were $5 for every head/tail/paw or some other disgusting thing I think I would be furious (ok know I would) but feral cat populations are dangerous- they grow insanly fast, produce animals capable of carrying TONS of diseases, and very quickly illimate all food sources for themselves, except garbage, getting into other pets food, and breaking into houses (yes, my house and kennel has been broken into numerous times by feral cats) they are starving and freezing/overehating and misserable- at least this way they cross the bridge peacefully (if they are not gassed- if they are gassed I have a problem with this on a whole different level) and dont suffer anymore, and dont create more cats to suffer. Hopefully, some will be adopted, returned to original owners, or pulled by rescue groups, instead of getting hit by cars, eaten by dogs, shot by pissed off homeowners, contract rabies, die in childbirth..ge t trapped in a basment trying to get food..etc. all the ways a feral cat dies daily. Not to mention the toll it takes on rabbits, squirrels, and birds...
Honestly, if it gets them off the streets and into a shelter where they can be dealt with- either humanely euthenizes or dolled out to cat rescue groups/private adoptors, I am compeltely for it an applaud the mayors initiative. IMHO, of course.
EDITED to add: I do believe that there should be some discretion in this case, to make sure the animals are not inhumanly trapped, injured, or hurt in A.N.Y way shape or form getting caught, or the person bringing them in be prosectured. I also think they should contact cat rescues and allow them to pull cats from the vets office at free will.