The problem (to me) is it's often impossible to truly match the "original". The different materials, building methods, etc often create something that is close

The problem (to me) is it's often impossible to truly match the "original". The different materials, building methods, etc often create something that is close but not quite right. See the Washington Monument as an example. Using a contrasting architecture results in "yea it's different but we meant to do that" rather than a "we tried to make it the same but it's still different". See the Louvre's pyramid entrance as an example--and yes, I know that was controversial in itself, but I like it.