Yes, I do not believe that it should be illegal for individual citizens to go around doing surveylance of public places. However, I do believe that this practice should be implemented by governments with well thought-out regulations around it, so that it will work to keep citizens safe and to protect their privacy.
There is a reason it is called "public" you are out in the open and free to walk where ever and when ever with who ever you want. With that being said, many things happen in public, including photography whether it be still photos or videos. This "surveillance" is often mistaken for the mere fact that people have cameras now, whether personal or in a place of business for security. You make the choice to be out in public, you make the choice with your actions, you should be held responsible.
Individual citizens' surveillance of public places should not be illegal because it gives more evidence for whatever the case may be. For example, if I were to witness someone shoplifting, I may turn them in, but I don't have actual proof that they were doing it. There may be surveillance cameras around the store, but sometimes you can misinterpret things from those videos. It's a matter of the angle you see things from.
Just because in the media we see a lot of crimes/ attacks, doesnt mean the public should be banned from public places. It dont think surveillance of the public people can bring about a lot of change as we wont have enough time to stop what is meant to happen.