In order for this proposal to be seriously considered, I think it's necessary to cite many realistic examples where the current behavior is problematic enough to justify changing the current behavior, and that adding a str.chars() and eventually removing the ability to iterate over strings would provide a better fix than any existing solutions. Simply stating that much of the Python community considers the current behavior to be "somewhat problematic" based on previous suggestions is certainly not going to be adequately convincing, at least not to me.
But, even in the case that we are able to conclude that the current behavior causes significant issues that can't be addressed as well with existing solutions, I strongly suspect that this is going to be the case of change that is far too fundamental to Python to be changed at this point, even with a distant deprecation warning and many years of advanced notice regarding the removal/change after that.
I could be wrong, but the level of potential breakage that would occur seems to be on the level of Python 2 => 3 bytes changes (if not worse in some ways); which I suspect very few people want to repeat. Not to mention that pretty much all of the textbooks, documentation, and tutorials that cover Python fundamentals or have examples that iterate over strings (which is very common) would have to be updated. The argument in favor of changing the current behavior at any point in time, regardless of how far away, would have to be incredibly convincing.
For the time being, I'm -1 on both adding a chars() and an eventual deprecation => removal of iterating over strings directly. At the present moment, I don't think it's been clearly established that the current behavior is even problematic or wrong in the first place, not to mention problematic enough to justify a massive breaking change.