The question is a bit vague because it is a bit arbitrary what exactly constitutes studying. For example, I myself have not followed courses or read chess books so far, but I have watched many hundreds of YouTube videos (including recordings of lectures given at chess clubs for instance by Finegold, Yermolinsky, Bok and many others), and I have played more than twenty thousand online games (probably >30'000 across all sites, admittedly, most of those are 30 second games or shorter). Many of the games that I played I have analysed with the engine and opening explorer. So while this does not fit the "classical definition" of studying, it is very much work that aims to achieve a similar result.
Courses and books offer the advantage that they present information to you in a structured way, and that they force you to commit to actively studying chess. Nonetheless, if you dedicate a lot of time to an "unstructured learning approach" (as I have in the past), you may still get to very competitive levels.
If you play for fun, there might be no need to worry about your level and then there is no reason to study.
If you play to improve, it seems rational to study actively and to go for courses, books, lectures, etc., since I would guess that those allow you to improve in the most efficient manner.
Courses and books offer the advantage that they present information to you in a structured way, and that they force you to commit to actively studying chess. Nonetheless, if you dedicate a lot of time to an "unstructured learning approach" (as I have in the past), you may still get to very competitive levels.
If you play for fun, there might be no need to worry about your level and then there is no reason to study.
If you play to improve, it seems rational to study actively and to go for courses, books, lectures, etc., since I would guess that those allow you to improve in the most efficient manner.