In tea, also there is tea powder, which we use. In coffee also, there is coffee powder. Why don't we make coffee in exactly the same way we make tea?
It boils down to temperature (pun intended).
According to Wikipedia the ideal temperature to brew coffee is 200°F, which is about 93°C. That is, the temperature is a little below the boiling point of water (which is 100°C). That is just boiling the water and pouring it over the beans will result in too hot a temperature. With a standard coffee machine like this one
the problem is solved elegantly. The heating element makes the water boil. The water then travels up through a tube. This cools the water just enough, such that the temperature is about 93°C when it drips upon the coffee.
Tea, on the other hand, needs other temperatures. Some teas (black tea, Pu'er tea and herbal tea) needs boiling water. Thus one just boils water in a kettle and then pour it over the tea leaves.
See http://en.wikipedia.org/wiki/Tea for tea temperatures.
Coffee and tea are used for similar purposes (hot beverage with caffeine; flavouring in a variety of other contexts) but that is their only similarity.
- Tea is a dried leaf (which may be cooked, smoked, or fermented before it is dried).
- Coffee is a ground-up seed.
Tea has more in common with dried oregano, or with cabbage, than with coffee. Coffee has more in common with peanut butter, or perhaps powerded almonds, than with tea.
A better question would be "why is the way we prepare and consume these wildly different plants so similar?" It's a wonder there aren't more differences than the ones you've noticed.