I'm reminded of that Dallas Cowboys practice facility that collapsed. It wasn't designed by a civil / structural engineer but by some analysis guru that used all kinds of goofy analysis to justify why it should work.
Regardless of whether FEM is used, it connection design should always be supervised by a Civil / Structural PE. Because of this, I doubt if it will ever fully go FEM.
I have some experience with this during my time at RISA. The RISABase program (which has since been discontinued) was mostly an FEM approach to base plates. As such it was pretty useful for cases where hand calcs would be difficult. Think bi-axial bending, and / or misplaced anchor rods. That being said, there were aspects of FEM that really required engineering judgment to interpret what it meant. You'd get localized stress risers in some places. Very easy to interpret with engineering judgment, but really tricky to do programmatically.