Well, it turns out New York isn't alone. Atlanta's MARTA system (essentially a BART knockoff with less track) requires a fare for kids over 46 inches.
I still think it's odd to use height as the factor, but those extra two inches buy you a lot of time. A typical 5-year-old boy ranges from 41.7 to 44.2 inches, according to CDC figures. By age 6, the range is 44.2 to 46.9 inches. That means most parents can avoid paying for their kids to ride MARTA until at least age 6. (BART and Muni, in contrast, start charging after a child's fifth birthday.)
But there's a downside. MARTA only allows you to take two children with you for free (versus three in New York). I'm still not sure what that means for your third offspring — I guess you either pay full fare for the kid or pretend you don't know her. (Sorry, Lulu.)