For that matter, what's with these kinds of storm drains in japan? They seem like an expensive terror to maintain.
they're all fairly common in asia (seen them in korea as well). Keep in mind the roads are a lot narrower in asia, so these are mostly there because ditches are deemed a hazard due to amount of people walking/biking on the streets thanks to population density. In rural areas you'll see more traditional uncovered non-concrete ditches because there's more room.
Yes the concrete does break and it's fairly common for people to step in if they're not paying attention. In big cities most have normal sewer and overflow systems you see in most western cities. Also a popular place for drunk people to piss after a night of bar crawling.
Also constructing underground sewer system would be more expensive. These are usually in residential area that feed to the bigger waterways, and yes, narrower roads.