You can use the viewpoints of the main stakeholders to help shape your projects at an early stage. Not only does this make it more likely that they will support you, their input can also improve the quality of your project.
Gaining support from powerful stakeholders can help you to win more resources. This makes it more likely that your projects will be successful.
By communicating with stakeholders early and often, you can ensure that they know what you are doing and fully understand the benefits of your project. This means they can support you actively when necessary.
You can anticipate what people's reaction to your project may be, and build into your plan the actions that will win people's support.