Plus, the plural form actually includes people who don't identify as male or female, and an increasing number of my friends appreciates that.
For example, if there is a person called "pat" who prefers to identify as neither male nor female, do they prefer to be called "them" in the third person? Or do they prefer something like "hir" or "zee"? (which are alternate forms as far as I have heard).
I think that if this is a hard problem, it should be solved immediately, without resorting to arbitrary made-up conventions, like using "they" everywhere.
I'm not a native speaker, but I agree it happens to me more often that I read past a singular they without noticing than if it were an artificial word like hir.