I would like to add few more points to your discussion. Mainly because of the nature of the job, some of the executives do not function as project sponsors. In large organizations, top level managers are very busy with their activities and they do not have enough time to sponsor. Due to this sponsorship falls down.
I believe that getting an executive and involving them in the project is very tough job. Projects will have high success rate in the presence of a sponsor with their support and commitment towards the project. However, a sponsor is the key person who plays an important role in the success of a project. If an executive is forced to act as a sponsor, then achieving this level of commitment towards project may not be possible.