Earlier quoted context omitted.
Why is it a big improvement over 'they'? Singular they has become popular naturally, whereas 'ze' has existed for years without anyone naturally using it(except for trolls on the internet).
"They is having a great time." It does sound wrong for some uses of he/she.
The accord with the verb is still as if it's a plural pronoun. Just like with "you" which technically also used to be plural, doesn't take the old singular second person forms: "you have" not "you hast"