It occurred to me that one solution to the English pronoun problem is to simply drop them for third person singular. That is the only time pronouns are gendered, but it's also the only verb form that conjugates for most verbs. Time will tell whether "they" will be become both singular and plural (as happened with "you"), or whether the pronouns start being dropped, as often happens in informal writing: "Pat is a coworker. Eats lunch at noon every day. Goes home at five. Never varies the routine"
Reminds me of when my mom was on a committee to choose a textbook for Sunday school classes, and the priest nixed their choice because it used the word "God" too much .. by which he meant that it was pretty obviously trying not to use a gendered pronoun for God. But it sounded pretty funny the way he phrased it.