Two reasons: (Relatively) low cost of labour, and (relatively) high cost of electricity in the Philippines.
Note that "low cost of labour" doesn't only mean "cheap maid/helper will wash the dishes", it also means that you will be more inclined to do the dishes yourself.
As a first example, say you're a professional software developer in the western world, maybe western Europe, US or Canada. Your typical hourly rate will be around 100..150$. Doing the dishes manually after a dinner with friends will likely cost you 2hrs, and hence around 250$ of "wasted" time. The expense of a dishwasher machine at, say, 600$ is comparatively small. After 3 dinners, the machine has paid for itself (of course, you still have some running electricity/water/maintenance cost, but that's in the range of 5$ per month, so not worth mentioning.) That's why virtually everyone in the western world has a dishwasher machine.
Now, as a second example, compare that to the situation in the Philippines: You're still a professional software developer, but you earn 35,000 PHP per month: That's, at best, roughly 5$ per hour! That's a whopping factor of 20..30 times less than your equivalent in Europe or the US! So your doing the dishes after the dinner with friends only "costs" you as much as 10 USD worth of your time. Now, to make matters worse, the same dishwashing machine mentioned above that costs 600$ in the US will cost 900$ (40,000 PHP) here, due to stupid, shortsighted and outdated import tax regulations. Owning a dishwasher in the Philippines will cost you more than a month's salary, instead of just a couple of hours of work. See why it suddenly makes much more sense to do the dishes yourself (or hire a maid/helper to do them)?
I won't even get started about the additional costs for electric power, maintenance and water for running a dishwashing machine here in the Philippines - it would just further my argument a little more.
Disclaimer: I happen to be one of the few persons over here who does have a dishwashing machine installed in the kitchen. But we haven't used it even once in 4 years. Nobody knows how to operate it anyway, or where to buy the required detergent and cleaner. The maids are doing a great job at washing the dishes.