Hi Ermeny, that's a key question specially in these times when so much technology is at our fingertips.
Obviously if you are living in the country where the language is spoken, it's much easier to practise and be continually learning and improving. Maybe in this case you don't have to "study" as such with a tutor.
On the other hand if you want to pass some official exams or you have some special objectives in mind, or if you want to make progress faster and have a limited amount of time in the country, having classes is the ideal way to move in the right direction, as you may need more academic input.
Having lived in Spain for many years, I have improved my spoken Spanish working and speaking daily with people you meet in every day situations, like work, friends, etc which really helps you to improve all round.
But when you don't live in the country, and /or you don't have people to practise the language with, I think a teacher really comes into his/her own. It could only for maybe an hour or an hour and a half per week for example. It's a time you as a student can touch base with your teacher, exchange ideas, you can share maybe problems /misunderstandings you have come across possibly during your self-study period, as there are lots of ways of studying and improving your language skills on your own these days, like watching films, reading articles online, reading books, practising vocabulary, and there are endless apps available.
Having someone to give you a regular boost of encouragement, and giving you some regular pointers all help to a more positive and productive learning language experience to my mind.
In addition it's not the same writing and listening to the language as actually producing it and having that personal guidance and assistance.
I'd say language tutors still have their place in achieving fluency.