...since I think their MESSAGE is clear enough
Perhaps you should have been clearer. This is a music video. A song. It is a lyrical paraphrase.
If the question is "how to deal with criticism?"... then this is what your question should have been.
Criticism is not "voices in your head". It is others people's voices. Other people's opinions.
Now, there is such a thing as "free speech". It is a very important topic, espcially in US culture, even if there are different opinions just what is or isn't meant by that term and in what way this "free" speech shouldn't be "free".
But the topic itself is still there.
Now your question "Should there be some level of Emotional Intelligence that moderates the ways in which people choose to criticize others?" is a valid one. But it doesn't have anything to do with the "voices in your head".
The answer is of course: "Yes, there should." But now the problem is: what levels, who decides on these levels, and how do we get other people to agree with that?
It is a valid question: "Should people consider how others perceive what they say, and adapt their words accordingly." I think it is a
very valid question,
especially in this context here. But I already know that you have some diverging opinions on that topic.
Still... no "voices in your head". If we dimiss the topic of mental illness and audible hallucinations... or even the option of supernatural outside influences... then this might be interpreted as "how do you personally interpret and process what you get from other people".
This again is an interesting question, but in this case, it is only the individuum who can find for themselves a solution. Over anyone else, you are the one who influences your own thoughts.