the lord of the rings - Why didn't the Uruk-Hai use Wargs to deliver Merry and Pippin?

In the movies, the pack of Uruk-Hai capture Merry and Pippin, and are bringing them back to Saruman as quickly as possible.

Why didn't they use Wargs to carry the Hobbits instead of packing them on their backs?

Or, better yet, why didn't the Nazgul fly down and take them on their Fell Beasts?

Answer

It mostly boils down to the different orc factions not trusting each other.

The Two Towers itself gives a partial answer, about the Nazgûl at least (emphasis mine):

'I am Uglúk. I command. I return to Isengard by the shortest road.'

'Is Saruman the master or the Great Eye?' said the evil voice¹. 'We should go back at once to Lugbúrz²'

'If we cross the Great River we might,' said another voice. 'But there are not enough of us to venture down to the bridges.'

'I came across,' said the evil voice. 'A winged Nazgûl awaits us northward on the east-bank.'

'Maybe, maybe! Then you'll fly off with out prisoners, and get all the pay and praise in Lugbúrz, and leave us to foot it as best we can through the Horse-country. No, we must stick together.'

^{_{The Two Towers Book 3 Chapter 3: "The Uruk-hai"}}

A fight later breaks out between the Mordor and Isengard factions, and the Uruk-hai assert their dominance.

The bottom line seems to be that, assuming we can take the word of the Mordor Orcs, there actually is a Nazgûl waiting to take the Hobbits back to Mordor, but the Uruk-hai are intimidating the others into taking the Hobbits to Isengard.

It's also possible that Grishnákh was lying about the Nazgûl waiting for them on the River - hardly a stretch to say an Orc lied about something. In any case, Grishnákh himself gives another answer for why they don't use the Nazgûl (both for this mission, and for other purposes in general), later in the chapter:

'But the winged Nazgûl: not yet, not yet. [Sauron] won't let them show themselves across the Great River yet, not too soon. They're for the War – and other purposes.'

^{_{The Two Towers Book 3 Chapter 3: "The Uruk-hai"}}

Basically, the Nazgûl are too busy preparing for the attack on Minas Tirith. This answer suggests that Sauron doesn't know that Merry and Pippin have been picked up, which is a possibility - the only orders anyone speaks of come from Saruman - otherwise you would think the possibility of recovering the Ring would be important enough to divert one Nazgûl from battle preparation.

The question of Wargs isn't addressed in the book, although I suspect the reasoning is similar.

Another thing to consider is that taking the Hobbits (and, in theory, the Ring) to Isengard is a dangerous move for Saruman to make. Since the Mordor Orcs don't like the sunlight, and since the Uruk-hai are clearly in charge of the operation, the lack of Wargs may have been a deliberate strategic move on Saruman's part to weed out the Mordor faction and prevent word from getting back to Sauron. But this is just speculation; The Two Towers doesn't address the issue, and I can't find anything in Tolkein's letters.

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¹ 'The evil voice' belongs to Grishnákh, a captain of the Mordor Orcs.

² The Orcish name for Barad-dûr