I think these methods of transportation are very much connected to the culture. For example, the first jeepneys were made from U.S. military jeeps that were left over from occupation after WWII. They've been adapted since then, of course, but the American influence still seems to be part of current Filipino culture. These vehicles also reflect the way the country deals with the massive traffic problem in Manila, as jeepneys offer a way of cheap public transportation, so commuters don't feel the need to own cars.
Trikes better represent the culture in rural areas, as these vehicles present a popular and convenient way to get around rural towns and on provincial roads. Trikes are essential in these areas, like Angeles City, where there are no taxis, and Grab, which is Asia's version of Uber, is basically nonexistent. Trikes also have the advantage of being able to weave in and out of traffic; travel on sidewalks; and drive down small back alleys. All of these tactics make the commute shorter, which is very necessary, as traffic is almost always bad, and people are often late as a result.
Another way both jeepneys and trikes reflect Filipino culture is seen in the way they are painted or adorned with things representative of their drivers. I have seen ones painted, for example, with an Asian Jesus and Hello Kitty. There are usually rosaries hanging from the rearview mirror as well, evidence of the fact that the Philippines is a predominantly Catholic country.
