Is there a Semisynchronous Buck Topology which mixes the advantages & disadvantages of both?
Partial answer - more later maybe:

I've seen parallel MOSFET and Schottky diode used in cheap Asian 12v_in to laptop (eg 19V) chargers. 

The disadvantages are largely the extra cost.   

A major advantage is that the MOSFET on/off timing becomes less critical as the diode handles the current if the FET is switched on late or switched off early.  As the diode handles current only at the switching edges (if at all) it may be rated at far lower mean current. 

I have also seen converters as above with the FET and diode allowed for on the PCB but only the diode equipped.