[Bluestrike2]

The problem is solved, barring serious complications with your home's envelope, with mechanical ventilation systems that give you control over how and where air is being exchanged in your house, while filtering it as well. That's assuming your building envelope doesn't have any serious issues; if water is leaking into wall assembly because of a poorly installed roof or gutter system, for example, no amount of ventilation is going to keep things from rotting away in a few years.

Anyhow, although leaky houses can help deal with moisture, that's pretty much an incidental effect. Leaky homes also comes with significant expense in the form of heat loss, worsened indoor air quality, pathways for bugs to enter the home, etc. There's a reason why we've been moving towards ever-tighter houses, even with the upfront costs and effort required for air sealing, insulation, and mechanical ventilation.

In the GP's tropical climate, I'd expect that humid air leaking into the house does very little to actually dry out the wall cavities; if anything, there's a good chance that those leaks would do the opposite and support any mold growth.