I have a degree in Political Theory and Constitutional Democracy, where we attempted to understand the political and societal contexts of the sources we read. Much of what we studied was the negotiation, formation, and early politics of the United States and our Constitution, in particular the motivations for the American form of government. I am no historian, but I am familiar with the source material, and endeavor to provide a comprehensive response to this topic.
The short answer is that everything in the Constitution is a compromise. Some compromises were between differing political players (ala the "Great Compromise").^1 Some compromises were between competing states on the nature of equality.^2 Still others were a compromise between two separate fears or interests of government, and it is this final set which is most relevant to the questions here.^3
There was great fear of a tyrant, to be sure, and so government was set up to be in opposition to itself, divided amongst three departments,^4,5 with states having their own authority independent of the federal system.^6 It was assumed that the different departments would seek to enrich their authority, and so in this system, "Ambition must be made to counteract ambition. [...] If men were angels, no government would be necessary. If angels were to govern men, neither external nor internal controls on government would be necessary."^5 Whenever there are contravening interests, though, there is almost certainly a delay in the speed which you may respond.
Deliberative bodies like the legislature are not always in session, and, even when they are, they deliberate. There is a need for "energy" in the execution of the law, and a political alacrity to respond to unknowable issues which lie ahead.^7 Under the system of the Articles of Confederation, there was no executive who could act with "energy" to respond to a political or military crisis, there was no mechanism to act swiftly and decisively.^8 Moreover, by placing the law in several hands, and the execution in a single hand, they can make a broadly-agreed upon law, but then place responsibility for enforcing it in only one person - if you have ever been on a committee, you understand how many people trying to do one thing doesn't work in a crisis. They also desired that the president should be indirectly-elected to mitigate the worst excesses of a demagogue who inflames a few states, through a more deliberative body: the Electoral College. (Although seen as an anti-democratic instrument, it was another attempt at moderating the non-angelic tendencies of humanity, because the Framers did respect the potentially-awesome power of the executive.)^9 Similarly, when these deliberative bodies are not in session, there is a need to keep the organs of government in operation, and the President has a single-person power to make recess appointments as necessary, rather than tying them up in committee (as is done with the Senate-confirmed appointments).^10 Meanwhile, there were extraordinary steps taken to distinguish the president from a king, with many limitations strictly delineated^11 to address the fears of several writers^12 that a strong executive is anathema to a republican form of government.^14 Perhaps the most important and indivisible duty of the president is to be commander-in-chief of the military, to make "the buck stop here," when it comes to balancing political objectives with military might.^15
In other words, the Framers made the Executive an individual because it was better to place limits on an individual who will then be able to respond in exigent circumstances, than to make a many-parted executive who could not sufficiently respond.
I hope to have given you a good place to continue your reading. It is difficult to summarize a whole series of essays on the Constitution, and to distill their writing into a simple summary for this medium, and I apologize for my relative lack of experience. This comment doesn't even address (except in the Endnotes) the contemporaneous opposing essays regarding the Constitution, and the "anti-federalist" reasons for opposing the structure or design of the new Constitution, but the question already posited some familiarity with these topics. If you have any more specific questions, I shall similarly endeavor to respond, below.
Endnotes
1 The Great Compromise
2 Madison notes
3 For all references to the "Federalist Papers," please find them at the link given here, referenced by "Fed #" in my citations.
4 Fed 47
5 Fed 51
6 Fed 46
7 Fed 23
8 Fed 24
9 Fed 68
10 Fed 67
11 Fed 69
12 The "anti-federalist papers" come from several authors, and are quite numerous and diverging in opinion. I hesitate to do so, but have decided to link to a Wikipedia article which references in parallel Federalist and Anti-Federalist works for comparative analysis. You may find the article here. See particularly Cato V.^13
13 Cato V.
14 Fed 70
15 Fed 74