First, Asia is varied and each individual country that makes it up is distinct, from culture to language to currency, religion, beliefs, political systems, socio-economic structures, economies, the way we look, eat, dress, etc, Each country pretty much has little to do with one another.
Second, that means a website using the .asia domain will have an unclear audience. Uzbekistan, for example, is in Asia. So is Iran, and yes, the Philippines. Even within just SouthEast Asia, there is little to share. I’m sure people in Myanmar and Brunei have about as little to share with me here in the Philippines as I do with those in Laos and East Timor.
Third: Conversely, creating a website or a section of an website that makes content for an international audience makes far more sense. In fact at the moment, a lot of websites already do this using either subdomains (http://philippines.domain.com) or subdirectories (http://domain.com/philippines), which can even be extended to specific sub-regions or cities (http://domain.com/philippines/cebu). In fact, why not get a new domain just for that purpose (http://www.domain-ph.com). These techniques perform essentially the same function.