Rather than Anglicizing it into...would actually take the song out of context and simply fail to do it justice.
And would, in a way, take it over for yourself without having to give due to the people it came from.

But that's just what Anglicizing in the old guard British tradition is, isn't it. It's a great tradition, old boy. It's more than language; it's culture in general. "We" are Greenwich Mean Time. "We" are the default standard of the world—people shall conform to us, not we to them.

Just look, for instance, at the South Asian ethnic communities in the U.K., as compared to North America and other places. In the U.K., Indians typically don't even say their own names right, because they have caved to whatever the Anglo society is expecting. I'm not talking about just saying it with English accent (which is completely reasonable in English context) but changing it into funny other things. Yet in the States the Indians just say here's how to say my name and the local people say it.

So, the "rules" seems to be:
1) WE shouldn't have to budge from our way. And those among us who do condescend to the level of the Natives of elsewhere, when doing their thing, are traitors and fakes. Yes, we will take their thing that we like, but only in properly Anglicized way...knife, fork, and all.
2) YOU should not try to do things our way, because you'll never be us, we'll never consider you to have truly gotten it (how can you capture our essence when your essence is different?). Our status as the default shall be maintained, and others will diverge from that accordingly.

An extreme caricature I've made, to be sure. My aim is not to create a straw man or overgeneralize a group of people.

It's rather to suggest that there is a worldview shaping this sense of propriety when it comes to singing and accents. And it's just *one* worldview. There has been a claim that Scots would be angry or put off or something if a non-Scot sang a Scottish song in a Scots accent. OK, they have the right; better to be pissed off than pissed on, I guess. But so many other people or the world, in the same sort of scenario would be THRILLED to have someone make that gesture. Plenty would not even think about the accent at all. For example, so long as the words were comprehensible, they might be focused on the meaning of the words, or the passion in the singer's voice, and might even feel honoured to have that.

The main theme I've been yapping on about is that if changing accents is a violation of one's aesthetics, so be it. It's a valid preference. Don't sing in a different accent, don't put your elbows on the dinner table, and don't forget to say "Excuse me" after you fart. But it is quite illogical to apply those "rules of etiquette" (of sorts) to what other people are doing in this big wide world. The default position is an illusion.

Excuse me!