tolkiens legendarium - Why aren't there any sieges in Lord of The Rings?

In the few cases a fortification is attacked (Helm's Deep, Minas Tirith), the attackers don't besiege them, they start an assault as soon as they arrive.

In real life, assaults were only done when, after a long siege, the defenders were weakened enough (or when an overwhelming force was really in a hurry, and a very small fort was blocking their way), and even in those cases the casualties on the attacker's side could be an order of magnitude higher.

As neither Sauron nor Saruman seem to have any supply problems, why don't they besiege the fortresses of their enemies properly? Setting up a siege camp, complete with a palisade to guard against a cavalry charge, then slowly and meticulously grinding down the defenses (or just starving them out) seems to have had a high probability of success.

Was Sauron really that overconfident and impatient? Is there an in-universe justification for this? Sauron was gathering his strength for thousands of years, so a few months more shouldn't be such a big problem. He also doesn't seem like someone too stupid to think about how a proper siege has to be organized.

Answer

There are a few reasons:

• Sauron is REALLY afraid that at any moment his opponents will use the One Ring and become much more powerful. He currently has the advantage but he might lose it at any moment, so he attempts this blitzkrieg instead of a regular siege.


• Mordor's orcs are too undisciplined for a longer siege: sooner or later they would start fighting amongst each other (if they didn't have an opponent to fight), which means every day would reduce the power of his troops.


• Minas Tirith is a fortress, which means it is prepared for a long siege with supplies (or even inner source) of food and water. His huge army would have serious problems providing logistical supply.


• He has a huge advantage of numbers and power so he believes in a quick victory.



• Taking the city quickly would give him a chance to defeat Gondor before Rohan would have a chance to respond.

• Saruman is confident in the power of his new Uruk orcs and his technology. He also has a cunning plan to break the Helm's Deep fortifications.


• Saruman probably wants to show off to Sauron, possibly to prove that he would not be a mere servant but maybe someone with almost equal power.


• It would look VERY bad for him, if Sauron had taken Minas Tirith quickly while he was still besieging the Hornburg.


• (As pointed out by @Scott) Saruman had Éomer exiled, greatly reducing the number of cavalry in Rohan's army. But exiled or not, Saruman could safely assume that Éomer would probably return (even without Gandalf's guidance) to harass the besieging orcs. So a quick attack would have greatly reduced the defenders' power and Saruman's losses.

In other words, both Sauron and Saruman have solid reasons for a quick attack instead of a long siege.