The first verifiable use of singular they for when the gender is unknown was in a novel some 100 years ago. The concept of ‘they’ as a personal pronoun was only developed in the latter half of the last century in the UK and has only been formally taught there for about three decades.
I think I would prefer two new sets of pronouns: one for when the gender is unknown, and another as personal pronouns other than he/she.
One could also think of they as that new pronoun. A lot of languages reuse sounds (including English) even in fairly common grammar components so one could think of this as a new word with a familiar sound assigned to it.