Something I've wondered about is the fact that a lot of no-kill shelters must turn away a great number of pets, any that aren't adoptable. That leads me to wondering if it's stressful to all the surrounding shelters that have to deal with extra intake of pets. I suppose it depends on how the 'no-kill' is run. There's no set definition, as far as I know.
My city has the largest cat sanctuary in North America for all the non-adoptable cats (and for many other cats simply because there are too many vs demand), about five years back the sanctuary won the bid on the city shelter, taking it over from the SPCA. They then made the shelter no-kill, and it's worked. Of course, they have a massive cat sanctuary to back it up, and are a large organization. There's also mandatory spay/neuter bylaws in place. The cat sanctuary was once at over 900 cats. Now it sits at around 700, so something must be working.
It would be a lot of work to get to that point considering where a lot of cities are currently. I live in a very wealthy city, and a lot of money and a shift in public opinion would be required for no-kill to start working in many other areas, especially in less well off locations, which are the areas where it's more desperately needed to get strays under control. It is doable, but it isn't something that can happen overnight.
So in short: I really don't know. Of course no-kill is fantastic, but if everyone tomorrow went no-kill, it wouldn't work. Maybe your area needs to start with something smaller (but no less difficult to implement) first, like changing public perception and getting more people involved in TNR.