I suppose I see the merit in teaching all music to all students in as many venues as possible. For students who have a musical intelligence as critical in how they understand information, the more music can be integrated into the curriculum, the better the chance they will have in feeling empowered in school. At the same time, I think that being able to learn from English songs in schools or countries where English is emerging can also be powerful from a social point of view. Much can be taken from learning songs by The Beatles or other songs in Asian schools. It can be an excellent representation of the globalized system that is a part of their learning setting. To be able to experience music from other cultures is an inseparable part of what the globalized setting is all about in the first place.
This is an interesting concept, and I'm curious what you're studying which prompts you to ask this question. It seems to me there's no harm in teaching songs in English to primary students in Asian schools; whether or not one should do so would, I think, depend on what one wanted to gain from this practice. If the goal is to help students begin learning the English language at a young age, it does seem as if this would be an effective way to introduce or enhance that process. On a personal note, I learned several French folk songs while studying the language more than 30 years ago, and I still remember them. My experience, then, is that using a song to teach or enhance language skills is useful and effective over time. If that's not the goal, however, you may need to re-evaluate.
Some Asian countries, particularly India, teach English as a compulsory subject in primary schools also. In addition there are many schools in which the entire education in school using the medium of English language. In such situation all students have to learn learn English language. It is quite understandable to include English poetry and songs as a part of teaching English language under some a system. This will give the student better understanding and appreciation of English language that they have to learn in any case.
However, I see no point in teaching English songs to students who neither know nor are required to learn English language. If, we are just talking about translations of English songs in local languages, then inclusion or otherwise of any such translation should be based on merit of such work, which has no relationship to the language of the original work.
Children are able to learn anything, primarily languages, when they are younger because of their neuroplasticity. Children have the desire to learn and teaching young children English songs may benefit them in the future because not only will they have their native tongue, but also another language to help them communicate with other people.
I would use childrens songs as a shared reading activity. Write out the works on chart tablets. As you sing you should point to the text so that they can follow along. This strategy is very effective with English Language Learners. It is interactive, and repetive and allows for many different teaching oportunities. Kinder and first grade classroom and been singing for years. Childrens songs include lots of expambles of alliteration, rhyming, punctuation, repetitive text and sight words! They are also a lot of fun to sing. By the end of the week your students will be joining in and signing a long while they work on their literacy skills.