All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
First of all, the rule that you have referred to is correct in general, but the definition of that benefit which is predominant over the disadvantage does not depend on the whims of the people and their desires.
There is no doubt that there is no Islamic preponderant benefit that allows the Muslim to listen to songs accompanied by music. The example that you mentioned does not fall under that rule.
The fact that a person wants to learn songs whose words are permissible is not a preponderant Islamic benefit.
There are so many old and contemporary poems that are permissible and which one can benefit from without having to listen to music. Also, there are so many poets, authors, and writers who say purposeful statements from which one can benefit in this context.
In addition to this, there is no Islamic preponderant benefit that makes it permissible to see forbidden movies. Indeed, it is not permissible for a Muslim, even for a specialist in film production, to listen to or watch those forbidden films.
For more benefit, please refer to Fataawa 342826 and 360949.
Allah knows best.