Is intrinsic motivation always a good thing?

Intrinsic motivation occurs when we act without any obvious external rewards. Individual simply enjoys an activity or see it as an opportunity to explore, learn, and actualize one’s potentials. People who are intrinsically motivated would pursue the activity for the pure enjoyment of it and engage in the behavior entirely from within rather than out of a desire to obtain external rewards such as money, prizes, praise, or reclame. Thus intrinsic motivation is usually considered as the best condition when people are doing things.

I wonder whether extrinsic motivation could lead to desired outcome which is beneficial to individual development. For example, a middle school student might be very intrinsically motivated to do exercise books and answer questions. The student won’t not gain any extrinsic rewards like desired high score or teacher’s praise. Suppose that what if the student just enjoys the process of figuring out questions and feeling safe when all answers aligns with the standard criteria. To some extent, it is just a tendency of mechanical operating and repeating in a learning context, which is more likely to lead to shallow processing thinking process. Life is complicated without an certain answers for any conundrum. The thinking habit of always seeking for the right answer could be benign to a sustainable thinking development, for individuals would confront struggling time with uncertainty and crisis. 

However, I wondered whether this learning style is indeed intrinsically motivated. For I experienced the above process during my middle school life, which could be very common at that certain age under that educational system (testing and enrolling). The ends in view were getting good grades and getting into a ideal educational institution. Nevertheless, I just realized that the process of answer questions correctly could authentically bring satisfying internal sense of achievement which drives me to move forward, which a fixed pattern (do exercises and check the correct answer). Admittedly, this might be a byproduct of the behavior (i.e. doing exercises), which was aiming at external rewards, getting good grades and then get enrolled. But take that single mode of “practicing” (it is could be learning but I would prefer to define it operational practicing), it could be intrinsically motivated thing, but it could rigidify individual’s mindset. I wonder it if the drawback of doing something which is intrinsically motivated when it is pondered on a cognitive perspective.