The Polygon to Raster tool should have more options and a richer ruleset to specify how grid cells are assigned polygon values, and more user options to specify the desired contents of the output raster values.
1. The user should have more control on how and when a polygon value is assigned to a raster. User input should control what percent of a grid cell needs to be occupied by a polygon in order to receive the value (e.g. user input of "0.4" says that at least 40 percent of a given grid cell must be intersected by the polygon to receive its value). (A similar option should be applied to the Polyline to Raster tool to specify the minimum length of a line within a grid cell for the grid cell to receive its value.)
2. The user should be able to specify additional output values. For example, a desired output raster value could be the area of the grid cell occupied by the polygon(s) that intersect it. This output raster would then have value for other geoprocessing that is not currently performed by the software -- for example, we could then use the FocalStatistics tool to calculate the total area of all features (say, cultural resources sites) that occur within a user-defined neighborhood of each grid cell as an indication of cultural resources sensitivity.
The software probably makes these calculations anyway, and capturing them should not cause much additional processing overhead.