Its not important but every teachers want their child lo learn effectively so I don't know about others ,but  being a teacher I use to give homework. And homework is not a burden it is fun because you are doing something you want to do because you are interested in that subject .

So I feel homework is nothing but a kind of bridge between you and your goal.

It really depends on the student.

Some students expect to avoid even the minimum of work during the lesson, let alone homework. Other students expect to have homework as a reminder that they need to study. Some students specify what they want to practice on: "please give me a writing prompt about xyz", "please give me more drills on tenses", "please give me some listening exercises" .

As a language student myself, I always expect homework. I can do my own reading, listening, googling and online quiz solving, of course, but I find that having a reference framework helps me focus and become more efficient.

@Wanda Embar

Not all students can focus and manage a learning plan of their own. Some need detailed instructions, step-by-step guidance and constant monitoring. This doesn't make them less successful learners in the long run.

@Alexander
" how is he supposed to know wether the student understood or didn't understand the topic"

A self-motivated student will let the teacher know whether or not they understood everything and if they didn't, will ask questions. I study on my own and when I want help, I ask my teacher specifically what I need help with. I don't need anybody giving me homework.

What you mention in your article as homework, are all things I do on my own, because I want to learn and improve. I really agree with your line "The most successful students who want homework outside of class choose what they want to do and then get guidance from their italki teachers." Exactly! Teachers are perfect for offering guidance when needed, but the drive to learn has to come from you.

Learning a language and using it naturally require consistent study and practice. How students practice is critical to acquiring functional language. Traditional language instruction fails to produce natural ability in over 85% of students. It's not because learning is necessarily hard, it's because traditional instruction methods really don't work. They focus only on conscious processes and do nothing to help the brain develop the ability to process language subconsciously, like everyone can do with their first language without ever studying grammar or memorizing a single word. 

In my experience as a teacher, students need carefully crafted practice activities to help them train. Without carefully guided practice, students can actually inhibit their acquisition of fluency. Call it 'homework' if you like, but I prefer to call it learning, and that is something that students must do on their own.