I do not think I would say it is the most important part of a project. The parts of the execution process that you mentioned are very important, although other parts are as well. Those parts are a necessity when it comes to execution since otherwise it could not be done. Those parts of execution dictate what the rest of the execution phase will be like. Planning could be skipped but the project as a whole would probably end up terribly. Each part of a project sort of paves the road for whats to come next, which makes every part important to one or more phase of the project.