Disclaimer: Frankly, since I was registered to this site, I was thinking on answering this very question. So, here you will see the answer in a while. Most of you very probably will not like it. Still, I will also disclose the fact how you like it at first place. That's all science of coffee.
It's widely known that, historically Turkey is one of the hubs of coffee trade and well-known for the Turkish-style brewing. However, this tradition is unfortunately not the best-known thing among the population in these days. Worse than that, the community is not self-aware of this. So, big merchants are using such ignorance as a benefit.
A few big roasters and coffee-houses known to prepare Turkish-coffee are somewhat built a monopoly on beans. The beans are mostly imported from Brazil and mostly the cheapest batches that are molding to keep the prices low. You can see two photos of some randomly chosen beans from a bag. These are six beans out of thirty, so the bad bean rate is around 20%. Imagine, when Ernesto Illy once said that one bean out of fifty in a cup spoils an espresso.
Then comes the roasting. Luckily, the big roasters have nice roasters for big batches. However, if you are visiting a small local coffee shop, it is possible that they have still using a pan to roast and burning the flat side of the bean and cannot roast the curvy side.
Below, you can see a photo from one of the most popular shopping malls of Istanbul. You can clearly see the uneven roast. I don't even discuss the storage conditions here! The damp, the light, the air...
Of course, the roast degree... Normally, cinnamon to city roast is the advised degree for proper Turkish coffee. However, bulk producers mostly goes beyond first crack, even to the second crack to hide the moldy flavors. The result is more like Vietnamese style; very dark roasted charcoal flavors. This is not what it used to be. However, the packaged roasted and ground Turkish coffee is mostly that.
So, the question remains, what makes it special? How do you feel a mouthful when you taste it at the headquarters and cannot reproduce it at home?
The answer is, freshness. That's what you feel, in my opinion. Most bulk roasters do not even care about degassing as they are selling anyway. (This may affect the taste, I assume. They start grinding right after roasting to get rid of stock expenses.) They sell to the tourists or to the ignorant Turkish population. Still, at the end, when you visit their headquarters, you smell a very fragrant coffee flavor. This adds to the aroma you taste. (You know, they say onion and apple taste the same when you don't smell them.) Then, you drink a very fresh cup of coffee. This is very probably nice as it is just roasted, even if the beans were bad.
However, you buy a bag of very fine grounded over-roasted bad coffee. The bag itself does not have a one-way-valve or it is not filled with inert gases or it is not vacuum packed. Thus, it goes stale very rapidly. Note that, fine grounded coffee goes stale more quickly. Even during your trip to your home. So maybe you have one or two days to finish the bag, if not a few hours.
TL;DR There is nothing special about Turkish coffee. It goes stale stale just so quickly as it is grounded so fine. Commercially marketed Turkish coffee bags contain crap.