Why is it necessary to "translate" songs to Mandarin that are written in Standard Chinese, but originally sung in Cantonese? Take, for example, the chorus to Beyond's 喜欢你.

喜欢你 那双眼动人 笑声更迷人
愿再可 轻抚你 那可爱面容
挽手说梦话 像昨天 你共我

As far as I can tell, the lyrics are in Standard Chinese even though they are sung in Cantonese. I see nothing particularly Cantonese about the grammar or vocabulary here. Would it not sound idiomatically correct if one tried to sing the same lyrics with Mandarin pronunciation? Instead, the so-called "translation" is this.

忘记你
美丽的眼睛 温柔的声音
我答应 忘记你
脆弱的背影 我们的故事
我努力 忘记你
For your example, it is more like 2 different songs based on the same rhythm rather than translation, because the meaning of the lyrics are far from each other. And for the reasons we redo the lyrics in Mandarin:
a) Sometimes, the pronunciation of the original lyrics in Mandarin doesn't fit the rhythm.
b) Some of the expressions used in Cantonese are not commonly used in Mandarin, like in this example: "愿再可", "你共我" are not standard expressions in Mandarin.