Having read over Hoard of the Dragon Queen and Rise of Tiamat, the reason for this path appears to be pretty well spelled out in the book, and that is secrecy.
Note on HotDQ page 5 under the header "Secrets," it states that
The Cult of the Dragon has kept secret its goal to bring Tiamat into the world thus far.
The Draakhorn begins to sound in Rise of Tiamat, no one knows what the Cult is up to or where they are up to it.
Note the focus on secrecy throughout the caravan's route. The treasure is:
Hidden in unmarked freight wagons among all the traffic on the Trade Way to conceal its nature and destination (p.28). Having booty streaming directly from attacked locations straight to their hideout would be pretty obvious.
Also, the cult doesn't have infinite resources. They have
Castle Naerytar, Parnast, and a friendly giant flying castle,
all of which also need to be low profile. Therefore, a plan of:
take the treasure, hidden in normal cargo traffic, to the "abandoned" castle, teleport it across a mountain range, then put it on a cloud castle and fly it to the Well of Dragons
seems like it's the best, absolutely most secretive way to throw off tracking of their activities. (In fact, it takes a party of 7th-8th level adventurers to finally crack this trail!)
A constraint on their travel relevant to their need for secrecy is that they can't just go anywhere with the treasure. If they just rode it due east out of Greenest to the Well,
they'd be going right past Darkhold, headquarters of the Zhentarim, who are aligned against the cult as described in both HotDQ and RoT.
In addition, you can't just run wagons over any bit of land you want; in HotDQ they make a big deal about very short bits of travel:
like the marshy 15 miles to Castle Naerytar, which takes 2 days for 15 miles, and that's only because lizardfolk have marked the trail.
By the logic in the adventure, you can't just go across marshes or mountains or deserts with impunity, so a caravan of goodies has to go somewhere such a caravan could reasonably travel IRL.
What other route would you take to maintain secrecy, given that you don't have infinite pick of hidden castles and allies, and given geographical travel restrictions? This one seems pretty good given the constraints described in the adventures.