It would be very nice to have shaping tools (intersection and trimming) to work as expected.

For this:
• When intersecting, leave both input objects (do not remove) and inherit the properties of the last selected object

• When trimming (cutting objects) cut the last selected object with the first selected. Leave both objects. Maintain the properties of the last selected object.

Very simple - the 'front-minus-back', 'expand appearance' and 'alt-clicking' tricks are confusing annoying and over-complicated.