Milhouse, your analysis is slightly off. It isn’t that the coffee does not exist!
Brochos 39a: Mei Silka K’silka-the water that beets were cooked in has the same berachah as the beets themselves. Basically, this means that when you cook vegetables in water, the water itself is infused with the essence of the vegetable.
This would apply too to coffee and tea and beer, EXCEPT –
Rosh explains that the water will only acquire a new Berachah-identity if, and only if, one is cooking the soup in order to eat the vegetables also. Therefore, by coffee and tea, when we do not eat the vegetables (pods / plants) the water/soup remains she’hakol.
Magen Avraham 202:22: Dried fruit such as apples, pears and plums that are poached in water you say “Borei Pri Ha’etz” on drinking their water (juice), and this is how I behave.
Even though coffee and tea are specifically grown and used exclusively as a beverage (which would cause a brocha of ha’etz or ha’adoma, in contrast to beer that barley is used not exclusively for drinking), the poskim state: brocha is she’hakol because the water is the main ingredient (see Shulchan Aruch Harav 202:12, Kitzur Shulchan Aruch 53:3, Yechaveh Da’as 4:42)