Why did the Sith need the Clone Army at all?

Question

During the Clone Wars, the Sith (i.e., Palpatine) essentially controlled both sides and both armies, the Droid Army and the Clone Army. The basic premise was that the Droid Army would weaken the Jedi by killing some of them, and later the Clone Amy would finish the rest (Order 66).

But why would the Sith need the Clone Army at all? The Republic has no other forces with which to defend itself. The Jedi were no match for sheer numbers of droids, as witnessed in the First Battle of Geonosis. Palpatine could pretend to be pacifist like Padmé Amidala and other senators who were against the Military Creation Act, but then the Army of the Republic would not be created, or this would happen too late to effectively train it and equip it.

Without a standing military, the Republic would quickly fall, and the Jedi would be killed more easily, and the Sith would rule the galaxy.

Why didn't Palpatine follow this plan instead?

Answer 1

Palpatine doesn't want the war over quickly

There are two main reasons for this:

1. As Jack points out in a comment on the question, the extended Clone Wars make the Jedi more vulnerable. This is discussed in the Matthew Stover Revenge of the Sith novelization; an inevitable consequence of the Clone Wars is that the Jedi (who never had terribly high numbers to begin with) are diffused throughout the galaxy, isolated, distracted, and vulnerable:

   With the Jedi Order overextended, spread thin across the galaxy, each Jedi is alone, surrounded only by whatever clone troops he, she, or it commands. War itself pours darkness into the Force, deepening the cloud that limits Jedi perception. And the clones have no malice, no hatred, not the slightest ill intent that might give warning. They are only following orders.

   ^{Revenge of the Sith: The Official Novelization Chapter 18: "Order Sixty-Six"}

   The other advantage of dragging the Jedi into a protracted war is that it delegitimizes the Order in the eyes of the Republic. Before the Clone Wars, the Jedi are a generally well-regarded organization; they're the moral authority of the government, essentially a state religion, and so effective at keeping the peace that they've largely supplanted any other Republic-wide defence force.

   But dragging them into a war they can't win (and Palpatine knows they can't win, because he ensures it), attacks the basic premises of their existence: how can the Jedi retain their moral unimpeachability while also waging a massively destructive war? How effective of a peacekeeping force can they be if they let this war go on for so long? Bonus points for Dooku, a prominent former Jedi leading the charge against the Republic. Even if you could simply wipe out in a single battle (a premise I find stunningly unlikely on its own), you wouldn't gain this advantage; destroying a Jedi Order still revered by the populace makes them into martyrs, which isn't what Palpatine wants.

2. One of the other goals of the Clone Wars was to delegitimize the Republic in the eyes of its citizens; this was accomplished partly by exposing the corruption and hypocrisy that already existed, but mainly by making everybody just so damn sick of the constant political turmoil; this is something Palpatine touches on in his Declaration of a New Order speech (again from the Stover novelization):

   "Never again will we be divided! Never again will sector turn against sector, planet turn against planet, sibling turn against sibling. We are one nation, indivisible!"

   The Senate roared.

   "To ensure that we will always stand together, that we will always speak with a single voice and act with a single hand, the Republic must change. We must evolve. We must thrive. We have become an empire in fact; let us become an Empire in name as well! We are the first Galactic Empire!"

   ^{Revenge of the Sith: The Official Novelization Chapter 19: "The Face of the Sith"}

   By making the Republic tired of war, Palpatine gets to assume absolute authority by promising peace and stability; this is something that's moderately easy to achieve after five years of constant warfare, but much harder to do if it's just a droid army attacking Coruscant.

Answer 2

Because Palpatine knew a slow, gradual takeover was easier than an immediate, hostile takeover.

Palpatine's vision wasn't one of militaristic takeover, it was one that was a lot more like the boiling frog metaphor. From Wikipedia:

The boiling frog is an anecdote describing a frog slowly being boiled alive. The premise is that if a frog is put suddenly into boiling water, it will jump out, but if the frog is put in cold water which is then brought to a boil slowly, it will not perceive the danger and will be cooked to death. The story is often used as a metaphor for the inability or unwillingness of people to react to or be aware of threats that arise gradually.

Palpatine knew that it was much more difficult to storm Coruscant and take over by force than it was to manipulate the Republic into appointing him ruler by choice.

Recall that the clone army was commissioned years before Palpatine/Dooku had convinced the Techno Union, the InterGalactic Banking Clan, etc. to join up with the Trade Federation and create the Separatist Alliance. Before that happened, all Palpatine had at his disposal was the Trade Federation's droid army and it couldn't even keep control over Naboo, let alone the Republic capitol of Coruscant.

Also recall that even with all of Palpatine's political manipulations, he still doesn't feel comfortable enough in his ability to maintain an absolute dictatorship until the Death Star is built and he decides he's finally powerful enough to dissolve the Senate.

Between the difficulty of taking the capitol, the unlikelihood of keeping the capitol, and the political fallout guaranteed to happen, it's quite obvious that manipulating the people into wanting Palpatine's control is much, much easier.

By slowly leveraging the Trade Federation conflict of Episode 1, creating the threat of war in Episode 2, and by painting the Jedi as traitors in Episode 3, he jumps to Supreme Chancellor, is granted emergency powers, and restructures the Republic... all with the cheering support of the Senate.

Answer 3

In addition to the points made by other answers, the clone army provided Palpatine with the following benefits:

1. By tricking the Jedi into fighting alongside the clone army, Palpatine was able to surprise them with Order 66 and kill almost all the Jedi at once. If Palpatine had instead attacked the Jedi with the droid army, he would not have been able to surprise them. Suppose Palpatine and the droid army attacked and conquered the Republic and the Jedi in a conventional battle on Coruscant, for example -- the Jedi would be able to anticipate their imminent defeat and would have had time to evacuate the Jedi Temple and send many of their members into hiding. By completely surprising the Jedi with an attack by the clones they fought alongside, Palpatine ensured that only the bare minimum number of Jedi escaped into hiding.
2. By controlling both sides of the war, Palpatine was better able to work around setbacks. For example, if the Jedi had discovered the inhibitor chip used to force the clones to carry out Order 66 (which they nearly did), Palpatine would have lost the element of surprise with Order 66 -- but he could have issued Order 66 early and had two armies (the clones and the droids) hunting down the Jedi.
3. As other answers have pointed out, Palpatine was able to paint the Jedi as traitors and delegitimize the Republic. As a result, the Senate and people of the Republic largely supported the creation of the Empire. This support was important because the Empire depended on the voluntary support of its citizens -- for example, the stormtroopers were volunteers. The Empire could have ruled with droids and clones, but it's much easier to rule when your army consists of volunteers. Moreover, while the Empire could have ruled without volunteer stormtroopers, it would have had a much more difficult time acquiring the expertise of scientists and engineers necessary to build weapons such as the Death Star. Galen Erso demonstrates the problem with coercing engineers to work for the Empire, for example.