No, the software development company should not play music in the development room. It is difficult to account for different tastes in music, and unwanted music is an intrusion that can negatively impact the concentration of the developers. You say that half of the developers have headphones on, which you assume to mean that they are listening to music. That means that half of them are choosing not to listen to music.
For developers, I don't worry about time that is wasted on something as trivial as selecting music to listen to. Development is an activity which requires a lot of thinking and analysis. The brain needs the opportunity to rest and not actively think about a problem, which makes it able to better and more quickly solve problems. The time that a developer is selecting music, unless it is extremely excessive, is an activity that lets the brain rest.
If your bandwidth is limited, and if usage of online music services is high, then that can be handled via a new policy that is communicated to the employees, and the online music service is then blocked by your servers. This is trivial to implement. Alternately, you could simply get better bandwidth.
If an employee is breaking the law by pirating music, then that is a matter to discuss with them (and, as above, block the site), and to consider whether to involve management, Human Relations, or someone else official to deal with the problem.
I'm unsure what you mean by "hearing power". If you mean that the employee won't overhear other conversations, then this might be exactly what the employee is trying to accomplish. They want to focus on their work, and conversations from others interrupt their concentration, so they wear headphones (which might or might not actually have music playing). If you are unable to get someone's attention when you need it, this can be alleviated by using other methods to get their attention, such as waving a hand in their field of vision. If you are concerned with your employees' hearing, that's really their concern and not yours.
Most importantly, consider the impact of such a change on your developers. If you are going to force them to stop wearing headphones while they are working, what impact will that have on their morale?
What is your goal in forcing employees to remove their headphones? If you want more control over how they are spending their time, you need to consider whether you are actually having issues with their output or whether you simply think that they could do more if they weren't wearing headphones. You should also consider why the employees are wearing headphones. If the work environment is distracting, headphones might be the employees' way of ensuring that they can focus.