Coffee Bags like Tea

The method of brewing you describe is commonly known in Poland, Belarus, etc, as 'Turkish coffee', althought it's something very different from the actual 'Turkish coffee', because coffee is poured over by hot water, like tea, and not boiled afterwards.

In fact, many people use sprinkled tea instead of express tea (express tea, or sachet tea is usually of much poorer quality). But many people dislike that method because of grounds that must be manually removed before washing the cup.

The grounds of the coffee are very small grained, so they won't stop the sink, and I suppose it's the reason there's not so much demand on coffee sachets. Another one is the popularity of coffee machines, with nothing similar in the tea world.

The last reason that I see is, because coffee grounds are much smaller, it's technologically more challenging to prepare coffee sachets that would keep grounds inside. So they would be (and from I've heard actually are) much more expensive, and not so many people are eager to pay extra for them.