Perhaps half of dog owners are responsible, and the other half are irresponsible, which is to be expected since there are not any tests of responsibility done on the owners of such. Because so many of today's inhabitants have moved into the city, more and more dogs now habitually reside also in city environments in which many of those people live in apartments, so that not only do a significant amount of dogs not have back yards, they also don't have space to run around in, and are often not even afforded even one good daily, comprehensive walk.
While all that is bad enough, dogs are animals, and animals have to defecate and urinate, in which, if the only space that your dog is basically permitted to be in most of the time is the apartment or condo complex, or a relatively small area of common grounds that you live upon, dogs are going to take care of their business where they have to take care of it, and while, no doubt, dogs can be trained for all sorts of things, mainly dogs are going to defecate when they feel the urge to do so. A responsible dog owner will then do their duty and clean up the dog excrement, since not doing so, especially in confined spaces that are heavily trafficked, could potentially create environmental problems that adversely affect human beings.
While there are myriad ways to attend to incidents in which dog poop has not been cleaned up, it is not too surprising that in a hi-tech world, DNA is one of those ways, of which, dogs are registered to each owner, a DNA swab is done of that dog, and when poop is discovered, a sample of that dog poop is sent to a DNA lab in which upon a match from that database, a monetary fine is issued to that dog owner. While that "solution" might sound wonderful to some people, it also sounds quite creepy and invasive, in addition to the fact that like anything involving tests, there are workarounds, of which, the simplest is to bring in a dog that looks similar to your actual dog for the DNA test to begin with. Another problem with this program, is the fact that not everyone is 100% competent in collecting dog excrement, and/or not everyone, especially when the weather is bad, or it is very dark outside, is capable of finding all of the excrement, or even recognizing from time-to-time that their dog has actually pooped, of which some basic consideration should be given for the fact that even people with the best of intentions, fall short.
So too, another problem with this stance of DNA testing, is that possible solutions for neighborhood dog excrement issues, don't need to be limited to just DNA testing, as a situation in which security cameras are utilized, good neighborly relations, training, and so forth, might be a better way to address a problem before it gets to become pervasive. Additionally, sometimes the easier solution of them all, is to make it part of maintenance's job to take care of dog poop as soon as it is spotted, and while this may seem like granting a green light for bad behavior by pet owners, isn't the real object of the exercise to clean up the common grounds for the safety of others, as opposed to confrontation and accusations.
Finally, there is one other consideration when it comes to DNA and the taking down of malefactors, which is today your pet, tomorrow, could such be utilized against humans in which the government is permitted to collect DNA from everyone in order to get a driver's license, employment, school admission, and so on.