While I feel your pain with regard to using an app like Splashtop or Team Viewer, I too believe to like the others here, that the iPad was developed with a touch screen to free one from the need of a mouse. The iPad was developed essentially to be an "all-in-one" "you don't need anything else to use it" device. Portability, ease of use and size were determining factors in the way it was designed,
After the iPad was developed, others saw ways that they could incorporate the use of an iPad with a desktop and that is a bonus, if and when it works the way it is designed to work. I don't know anything about anything, but I really don't envision a day when a mouse will play a prominent role in the use of an iPad. It's beauty is in the simplicity of use.