In general, intersection of inputs is the default extent for all tools. There are many tools involving points where this leads to truncated output. In these cases it would be more appropriate to have the default extent switch to something larger. In the case of the Watershed tool it should be the Flow Direction. For distance and density tools it is less clearcut, but it would make sense to buffer the points by a percentage of the extent or a fixed distance or something similar so that the user doesn't end up with truncated datasets. This could even be added as parameter in the tool overwriting the default extent.