Yes, GIS has been used. See for example ESRI's Lauren Bennett who has made presentations (refer to https://www.esri.com/about/newsroom/author/lbennett/)
I myself have used GIS for poverty prediction and population prediction (see articles on RG)
Yes indeed! this is less explored area of GIS application. Recently, there is increasing interest of scientist from spatial science and epidemiology and I hope more more research questions related to time/space dimension of epidemiology will be addresses in the near future.
In my opinion, they maybe don't fully understand the capabilities of using GIS.
Most spatial epidemiology is only exposed in the form of medical information systems and disease approaches but not in the context of geographical information.
GIS are powerful decision making tool when geographic distributions are part of the problem. It can put several elements together necessary for visualize, analysis and problem solving.
Epidemiology and Geography are separate fields that are gradually having a link to each other. Most geographers don't know epidemiological study designs and most public health practitioners have no knowledge of spatial analyses. Here is the reason why I moved from the Geography after my MSc to Public health for a PhD. However, interdisciplinary studies are bridging the gap gradually but it will take a long time.
I think lack of awareness among the scientific community about GIS. Those who have heard the name, think it may be a rocket science or don't want to to spend time on learning GIS. I think GIS is a tool which can be used in every field of research.