Although, are we really capable of moving enough water that distance to make a dent in a literal desert

more than you think

I did the calculations: to move the amount of groundwater present in continental US (30k cubic miles), you would need to run a Mississippi river for 200 years

The Taklamakan desert is the size of Germany
Germany is 4% of the US surface area

Mississippi moves 1.5 billion m3/day
Total desalination world wide purifies 95 million m3/day

global total desalination (half of which is literally just Saudi Arabia) is already 7% of the Mississippi River. (and We need 4% of the Mississippi River to green the Taklamakan over the span of 200 years.
Saudi Arabia moves around 3.5% of the Missippi River alone, lol.

This is very greenpilling. It's not the desalination of the water that's the point here, but rather the sheer MOVEMENT of water. There is tons of other stuff (oil, gas, other water, other fluids) that are moved in huge quantities annually.

More Missippis = more fasterer = you don't have to wait a century

The Bengal Dam reservoir actually generates more water than the Mississippi, 200 cubic miles/year instead of 150/year.

So if China could build a trench that transports that water, the Taklamakan would turn into lush, green Germany in 6 years. If you split the water 3 ways between India/Pakistan/China, then 18 years.

Feasibility of building that trench, which basically would be an artificial river: I don't know. I intuitively feel that it's doable, and I feel that the rewards at hand would more than justify any financial sacrifice taken. We're talking about a country that has reclaimed from the sea, over 2 Puerto Rico's worth of land since 1950--I feel like they can definitely build a river from Bangladesh to the Tarim Basin.