Teapots and coffee pots are very different. Teapots In Europe came in the early 1600’s. Dutch traders brought it back from the orient and the method to brew it too. The English upper class were enjoying tea by the 1660’s. The Dutch-owned the market and in 1689 tea was taxed at 25% in England but the tax was reduced to 5% in 1692 So by the early 1700’s tea was widely enjoyed all over the world.
Coffee entered the European markets around the 1600’s coming up through Italy and to Europe. Coffee was brewed by putting it in a pot and boiling it. When pouring it out you did so slowly and tried to keep the grounds in the pan. Over the years there were many different tries at a mobile coffeepot. The first viable transportable coffee manufacturing device that was rugged enough was the cowboy coffee pot. Tapered sides to keep the grounds in the bottom and a crude filter in front of the spouts internal spillway. The spout being located towards the top of the pot, and a handle
And now the curmudgeon part:
All this is because boiled tea leaves float to the top and boiled coffee grounds sink.
Also, Coffee is the Second most traded commodity in the world only being surpassed by Oil.