Well, we can agree on that last point, certainly: nobody should ever not care about language. But that's not the same thing as "nobody should ever not care whether the words they use in any given situation are the generally accepted correct ones."

If words are tools with specific jobs, it stands to reason that there's nothing wrong with experimenting by applying a tool to a job it wasn't designed for; you may achieve something interesting at least, and you may achieve something spectacular. I once saw a guy hook up a power drill to a pepper-grinder, which did exactly what he wanted it to: it produced large quantities of freshly ground pepper very fast, a goal otherwise impossible for a single person, made easy by using those tools the wrong way.

Generally with words that's not going to happen, except perhaps in the context of poetry -- but I've seen works of poetry that prove that sometimes ignoring standard usage is the best way to convey meaning.

(I don't think this comic is an example of that. Beret Person is generally amusing and I'm fond of him, but I wouldn't take him as a role model, and I agree with your assessment that he doesn't really care whether he's understood.)