Learn English – Meaning of the sentence from the song “Powerless”

To understand what this simple phrase means first think of the literal meaning, that the person was abandoned because it was assumed that they were already dead, mortally wounded or that it was inevitable that they die.

But there is more to the phrase than that. In common usage, this phrase is often part of a narrative where a person was expected to die, yet against the odds they survived. Some examples from COCA:

Left for dead by a busy road, Susan managed to get a ride to a police station where she insisted she be brought to the Nairobi Women's Hospital.

Pueschel, just 11-years-old, was beaten, stabbed and left for dead, but he lived to testify against Reginald and Gerry Mahaffe.

... a young man in Los Angeles was robbed, shot, left for dead, but he lived because a bullet was stopped by a radio in his pocket.

The common theme in these stories is an act of cruelty towards an innocent person who survives either by a stroke of luck or a miracle. A proper reading of the title Left for Dead should include cruelty, abandonment but also a sense of hope.

I'm not an English major, but I am a native speaker.

"I'll bring you home" is definitely not invalid; it's a perfectly fine thing to say, and I think your meaning is correct.

However, "I'll take you home" does not imply that you live at the same place, or that you're going to be staying over. I think it just implies a sort-of dominance on the role of the speaker. I would imagine this being said by a person speaking to someone who is more drunk than they are, or by a speaker who knows the way home better than the other person. Although, to be fair, it probably depends a lot more on who says it, how they say it, and exactly how they phrase it and not so much on bring versus take. For example, "I can take you to your place" has essentially the same meaning as "I'll bring you home."

I think the most natural thing to say in the case that you are both going back to the same place, or both heading home is "Let's go home."