Whenever you run an analysis tool, the output is a new layer. For me at least, the majority of the time the former layer is useless after I've run the analysis. For instance, if I'm joining something, I just want the layer with all the fields, not the partial layer I added them on. If I'm enriching data, I only want the layer with the additional data. You get the point.
I realize that removing a layer from a map or even deleting it entirely isn't a huge amount of trouble, but it's just one more step you have to take, and one more barrier to keeping content, maps, and apps organized in terms of only having the layers and files they need and not letting old ones sit around.
I'm just picturing an optional checkbox or two in the analysis tool setup.
- Create new layer and leave existing
- Create new layer and delete existing
- Do not create new layer and overwrite target/existing layer