The underlying reason beyond the use of the たがる grammar is that in Japanese you can never speak in such a way that you know what another person wants to do. However, you can say that someone said they want to do something, or they seem like they want to, and so on. There are multiple ways to get around it, たがる being just one of them.
So, the だろうか (with emphasis from the もしかしたら, though it's not necessary) is accomplishing that. The sentence is "I wonder if it could be that he still had something he wanted to say?" As you can see, it's not saying what another person wants to do, it's just speculating, so it's okay.
Last edited by Tzadeck (2011 November 11, 9:58 pm)