Why do you think in the end the Framers had to include an executive branch of government?
In my opinion, the Framers had to include an executive branch because their government (under the Articles of Confederation) had been so weak without an executive.
Any government really needs an executive to be effective. There has to be some amount of centralized authority if the laws are to be carried out. You can't have Congress (or even one committee) in charge of carrying out the laws. It's just too inefficient when you have to have all these people agreeing about what to do. That is one reason why the Framers chose to have a single chief executive instead of multiple executives as some suggested.
Much of the Constitution was written to make the government less efficient and therefore less dangerous. But the Framers knew that some efficiency was needed so they set up an executive branch to carry out the laws.