No bleach! Starsan does not clean anything. You must clean then sanitize. PBW or unscented Oxiclean should work well if you soak it for a while and scrub it with the soft side of the sponge.
Yes!! The problem with using bleach on a regular basis, to sanitize OR clean, while at the same time using municipal water, certain minerals in whatever water you use and certain plastics, is that you could build up chlorophenols in your brewing systems, which could contribute to off flavors in your beer.
In some situations they work cumulatively by having little bits of chlorine in different parts of the brewing process that your beer may come in contact with, and it builds up and bammo plastic band aid flavor.
It's best to avoid chlorine as much as possible, and in the case of sanitizing ONLY in the most dire situations, like where you know for sure you have an infection.....we call it slash and burning.
I try to limit the amount of contact my gear comes to chlorine and chlorine products.
chlorophenols are funny that way, some folks aren't affected, and in other situations the right combination causes issues. I try to avoid it as much as possible.
And unfortunately my understanding is that folks have little control over is their setups can handle it. I've heard of folks being successful for years with it, then they replace one piece of gear like their autosiphon, or move and change water sources, or have new plumbing put in, and suddenly they have them now.