I know language evolution sounds like a weak argument, but it's true. They isn't even originally an English pronoun at all (it comes from Old Norse, the English form was hie)
Singular they doesn't bother me, since I think it evolved from the generic they (as in: They drive on the left in the UK). Personally it sounds weirder to me when they is used for someone specific, because of the history as a generic pronoun.
My personal theory is that we started using they as a gender neutral pronoun due to an old almost subconscious animate/inanimate distinction in the language (which is why no one adopted it as a gender neutral form)
Originally it was ye (you was the objective form) and the singular was thou/thee.
We have a lot of choices, depending on dialects: y'all, all y'all, youse, even yinz (from you ones).