What about replacing the jeepney situation with more modern busses like the ones in Korea and Japan?

Those buses are still too large.

There are already microbuses here (but they don't deserve being called "jeepneys"), however not all of them are able to access narrower streets or drive through rougher roads or ford streams in remote mountain valleys. That they are very expensive as brand new versus jeepneys, which are often bought and sold or traded even 20 or 30 years old and can still be serviced with existing parts.

That why with the driver behavior resembles so much like fishermen trying to catch fish, it's literally every man for himself.

Having been on the street for years, and having seen the transport systems of, say, Indonesia and Vietnam and Thailand where there way more motorcycles than here, until there is proper public transport, we lower-class Filipinos have to put up with the chaos of not only individualized and fragmented transport systems but also the continuing demand for private transport whereupon well-to-do Filipinos shy away from mass transit but also the prestige of having their own car, and thus causing greater congestion issues than it was 40 years ago.