How could the Nazgul take Minas Morgul?

[Kuruharan]

But if the supply line goes unhindered for the most part, it is no problem to constantly ship things along it.

Unhindered by sentient beings does not mean totally unhindered. Broken transports, weather delays, the necessity of feeding the ones doing the transporting, rock slides, mud volcanoes...these problems become more inevitable and substantial with every mile you have to cross.

Let's take the time to look carefully at the map.

In an act of generosity on my part, we'll say that there are sufficient settlements just to the east of the Sea of Rhun, that is a distance of at least 600 miles.

The distance from Minas Tirith to Minas Ithil is about 45 miles.

Are you starting to see where we are coming from here?

I would think the Gondorians might have more difficulties having to haul things over the Anduin, while worrying about potential raids on the shipments from orcs and other baddies.

Nonsense. It was their river and they were a river people.

As for orcs and other baddies, there were no orcs or other baddies in that particular area at the time. That is part of why we are finding it so hard to accept that the Witch-king just created an army out of nothing and then laid siege for two years unopposed.