I too am seeking a solution for this. A most basic common task is to search for address using the world geocoder, the map zooms to the location and adds a marker to the map, and automatically displays a popup showing attributes from layers in the map at that location.
Using the search tool built into the map adds a marker to the map and zooms to the location, but then the user has to close the callout that appears on the map, and then has to click on the map at the location to get the popup. That is a lot more steps for the user than what they did previously in a WAB app I am migrating, and customers are not accepting it.
As a result I will have no choice but to modify the existing search widget, with EXB developer, but that code is nearly completely undocumented so its hard to know where to even start!
If someone has come across this already and has a custom widget or pointers for modifying the search widget code it would be greatly appreciated!