If driving is already so inconvenient why not just relegate it even further and prioritize walking over vehicles at intersections? Why should all the larger numbers of pedestrians be forced to take much longer to get where they're going on account of all these bridges to benefit a smaller number of vehicles?

Sure, improvements should be made. The pedestrian bridges themselves are improvements. People use them by choice, and not because they appreciate the exercise. It would be easy to underestimate just how many many vehicles and pedestrians are attempting to navigate the metro Manila area. Roads and other transit infrastructure are seriously lacking in Philippines, relative to that seen in more "developed" nations.