What you write doesn't refute the problem which is that countries like this generally have worse health outcomes, healthcare systems, they have fewer skilled workers to build their economies.
Skimming their best resources off the top can't be justified by some dry economic formula (if it happens to be correct) that just by pure coincidence results in a worse outcome for that poorer country and a better outcome for the wealthier one. Colonialists had all sorts of economic arguments too.
I would agree that the Phillipines are under-supplied according to OECD ratios but again, I don't think the problem is emigration.
Personally I think your mental model of these countries is out-of-date. They are sophisticated and industrialised but do have high inequality and some governance problems. As usual, it's a distribution problem. I think you are under-estimating their capacity and they are not at all lacking in talent, education or human resources. Australia is lucky to get skilled migrants but is by no means "draining" them. I think I'd want to see a more quantitative argument before I was willing to accept that.
I'm not saying some individual's story or a particular situation in a particular country is neocolonialism. It's the entire system of siphoning resources from disadvantaged regions to wealthy ones.
Skimming their best resources off the top can't be justified by some dry economic formula (if it happens to be correct) that just by pure coincidence results in a worse outcome for that poorer country and a better outcome for the wealthier one. Colonialists had all sorts of economic arguments too.