I've never liked this, but I have to admit that logically, a mismatch in number is no worse than the mismatch in gender we get by using "he," which has the disadvantage of being annoying to many people. And I don't think efforts to make up a new pronoun are likely to succeed. Singular "they" might well be the future. But if I could have my pick I'd go with "um."
As the article describes, singular they is also the past. Its usage has a long historical precedent over 650 years.