It's not illusory or an "artifact", since you can have electromagnetic field configurations that cannot be reduced to simple electrostatics (i.e., electric fiel

It's not illusory or an "artifact", since you can have electromagnetic field configurations that cannot be reduced to simple electrostatics (i.e., electric field but zero magnetic field) by picking an appropriate frame. Special relativity helps to explain why, even if you have a configuration that is purely electrostatic in one frame, it won't be purely electrostatic in other frames. But that's not the same as saying that all electromagnetic field configurations are that way. They aren't.