I, too, am a big fan of TTVNR (Trap, Test, Vaccinate, Neuter, Release).
In some instances, though, it might not be an appropriate solution if there is an immediate problem with a specific colony.
Also, it isn't as easy to set up for shelters at all... usually it is done in partnership with local 'gattare' or 'crazy cat ladies' who are the ones willing to trap, get the spay/neuter done and, most importantly, monitor the colony and care for it. Most shelters receive the incoming stray or whatever and then would rather just dispose of it than contract with people to deal with colonies... out of time/cost... (or so they think).
From my understanding, it's often hard to find people who can commit to being responsible for monitoring, caring for and managing the feral cat colonies--it's a daily job!!!
And, despite how much success many of them have had (College campuses being a good example, or San Diego...) many many people are ignorant and assume eradication must be easier, cheaper and better (even thought that isn't necessarily so or (in the case of eradication) even remotely possible) and so are against it. Others who disapprove are people concerned for songbirds, endangered birds and other local wildlife. That's why some shelters have a policy of euthanizing ferals... they don't agree with releasing these 'invasive species' back, even if some studies suggest that its ultimately the best way to decrease the colony/feral population size over time...
