It depends on the type of church setup you've got. I attend a smallish local church - tea and coffee after the service are provided by a rota of volunteers who provide an insulated flask of instant coffee and another of hot water for tea. It's definitely not the height of flavour but it serves as something hot and relatively palatable to drink while catching up with people.
One of the limitations of doing anything 'better' is the unusual characteristics of the demand. If we had the equipment to make really good coffee, it would be sitting unused most of the week - we have some mid-week activities but most of those take place in people's homes. Then, once a week on a Sunday morning, you'd have a sudden demand for lots of coffee in a very short space of time. At very least we'd need two or three large french presses and someone to look after them rather than the current 'self-service' approach.
The equations might be different in a larger church with more resources, better facilities and greater usage throughout the week but better coffee is not an issue we have considered working on. However, say a church was in a good position to run a regular cafe, I could certainly see that pressed into use to support hospitality around their regular worship services.
Wulf