Yes, there are downsides to the lack of exposure to other activities:
- The child may not get exposure to societal conventions or norms outside of their area of expertise.
- The child may not develop other skills, and thus lack options if they ever stop pursuing their current interest.
- Increased demands/expectations on a child that may have heightened intellectual capacity, but not comparable emotional or other neurological development. The added stress and exposure can lead to an increased risk of anxiety and depression in such children.
1 and 2 here also apply to children that spend too much time playing video games or watching TV (if watching TV could be called an expertise).
However, there can also be downsides to forcing your child to not engage in their chosen activity: They could be on their way to being experts and/or leaders in their field, and preventing them from pursuing their interest may hinder their development.
Some of my readings indicate that the key to raising prodigies lies in proper support for their abilities. If the parents can recognize that their child has that ability, and help nurture it, then the child can be largely successful and happy. The "dark side" of being a prodigy tends to occur when a child is being forced to work or practice, or doesn't get to have a say in what they're learning.
For your specific example of the prodigy developer, I think some of these points have to be thought about with the field of computers specifically in mind. My early point 1 may be largely irrelevant, as society tends to accept "geeks" of all levels of social ability. Point 3 may be mitigated some by the fact that most of their interaction with their "peers" will be through the Internet, where it can be easier to separate oneself emotionally.
Additionally, coding isn't a task that takes well to interruption. A 10 minute break may take an additional 10-15 to recover from and get back into the zone. The frustration of this downtime may be detrimental to the child's goals and progress.
Also, there are physical issues to be concerned about. It is not healthy for a child to be sitting in any given position for 3 hours straight, much less at a computer where their hands are performing repeated tasks. It's going to be very important for them to take adequate breaks and stretch. While it may not be the best idea to come in at specific times and say, "Take a break, now.", it would be a great idea to train the child to make sure they're taking breaks often, especially between tasks. It may also necessitate investing in a highly ergonomic work environment for the child, to promote the long-term health of their hands/wrists/spine.
In many ways, a child prodigy should still be treated like a child. Even if their abilities in their domains exceed your abilities, or even your understanding, you still have the ability to teach and guide them. They can learn things like time management, stress management, healthy habits, communication skills, emotional intelligence, conflict resolution, and more. Developing a framework, mastering the viola, or painting a masterpiece don't require any of the other skills I just listed. (No, not even time management! Focusing on one thing, and one thing only, isn't time management.)
Even if the child doesn't get exposed to other activities, they're working on something they already enjoy. It can be very hard for people of any age to find something their passionate enough about to devote so much time and energy to as a prodigy may. I would hesitate to put too much of a damper on that. Even if they change their mind later in life, they may have developed their particular skill well enough to allow them to do it as a job so that may use their free time to pursue other interests.