I can go this one-better. In my neighborhood we have PART-TIME reverse-angle parking. Only on Sundays and days designated by the Police Dept. Here is why:
The blue dots are all churches. (When the neighborhood was built in the 1930's, the developer donated land for new churches facing the 4 corners of the park; clockwise from top left they are Greek Orthodox, Catholic, Church of Christ and Lutheran.) The street on the south border of the park is a busy one, with a large Catholic high school 6 blocks to the east of the park. The Catholic and Lutheran churches also have grade schools on their campuses, and there is a public school just south of the Orthodox church on the opposite corner.
As you can imagine, the schools and the park generated a fair amount of traffic as time went on and more people starting driving their kids to to the private schools and park instead of them walking, so the city tried to allow for passing room when drop-pff lines totally clogged traffic. The streets have been converted to 4 lanes, but only the one on the south boundary is really wide enough; the others have very narrow lanes. Normal parking around the park is parallel parking so that there is still room to pass if a drop-off line is blocking traffic, but on Sundays that just isn't enough parking for the Church services. So, on Sundays parking on all 4 sides of the park converts to reverse-angle. (Parking on the opposite sides of the streets remains parallel at all times.) Police can also change it to reverse-angle for special events, such as school sporting events, weddings or large funerals.
FWIW, it's been this way for about 30 years. Locals are used to it, but it does confuse folks who come for special events. The city chose to do it that way here because the congestion was caused by church services, which people tend to leave all at once. Leaving was a lot faster when they were pulling forward instead of having to back out.
I have been told that it is the proliferation of SUV's that is causing this style to become more popular with traffic engineers. Now that so many people are driving vehicles with large, high backs, backing out into traffic was becoming much more dangerous because of reduced visibility.