You are hitting a system limit in what you are trying to do.
ArcGIS system fields, such as Shape_Length, Shape_Area, OBJECTID, have their attribute values maintained by ArcGIS and thus cannot be treated like ordinary fields in the way that you wish.
For example, if you were to spatially join a point to a line, and then the line is extended so that it is has a longer Shape_Length in the line feature class, then what should happen to the "Shape_Length" field whose values you transferred to the point becomes problematic. I see two options:
- Its values could be frozen - but you can already do this by adding a field and calculating it equal to Shape_Length prior to the spatial join (like @Barbarossa has suggested)
- It could have a dynamic link maintained but this would involve relating the line and point feature classes in something like a topology, geometric network or network dataset, and thus having them stored in a feature dataset.
For either of the above you would be looking at trying to convince Esri of the need to add this additional functionality to ArcGIS via ArcGIS Ideas . Option 1 above would be the easier to implement but it is so easy to workaround so there is little incentive for that to happen. Option 2 would have far reaching consequences so I think would stand little chance of being implemented, unless a compelling business case emerges to do so (which I do not see happening in the foreseeable future).