Hello,
wouldn't it be great if Esri developped a Web AppBuilder-Widget to change the layer list in combination with the background maps similar to the ChangeWebMap-Widget of the GeoNet-Community?!
ChangeWebMap Widget
In the web apps of the geoportal of Karlsruhe there are several needs to change the layer list and background map. I succesfully implemented the GeoNet-Widget in the menus "Themen" (english: "layer list") and "Zielgruppenkarten" (english: "maps for target groups") as you can see here:
ArcGIS Web Application
It works but the disadvantages are
- few configuration possibilities
- you have to create a web map for every combination of layer list and background map
- the order of the web map-list can't be defined
- the web app always restarts when changing a web map
- in case of problems after updates I would prefer to use Esri-Widgets to get full support
So please like my idea if you are also interested in such a widget 
Greetings from Germany