If I am not mistaken, parents in D.C. do have that option. The city sponsors numerous charter schools that a D.C. parent could choose from, if they so chose.
Charter schools are still government schools
Nor do the numbers above include private and parochial schools, or homeschooled kids. Adding it all up, I would not be surprised if regular DCPS have less than a 50% share of all k-12 students in the district.
The moral of the story is that failure is expensive. The average Catholic high school in DC is in the $12-17,000 range. A couple of the big names are in the mid-20's but only Georgetown Prep is over $30,000, and that barely over. I'm a little rusty on the numbers and don't feel like looking them up tonight, but iirc, the Catholic elementary schools are typically in the $3500-8,000 range, with most (I'd guess) toward the lower end of that range. The big name secular private schools are a bit higher. On average, however, DCPS is more expensive per capita than private schools, despite Sidwell, St. Albans, NCS, etc. pulling the average up.