What would the pros and cons be of this 'zig-zagged' high-sweep wing planform?
That's called sweep variation along span. What you've done is combine an inner W wing with an outer M wing.



Both of which were never used.


  
  W-wing: A reversed M-wing. Proposed for the Blohm &amp; Voss P.188 but studied even less than the M-wing and in the end never used.
  M-wing: the inner wing section sweeps forward, and the outer section sweeps backwards. Allows the wing to be highly swept while minimising the undesirable effects of aeroelastic bending. Periodically studied, but never used on an aircraft.
  


The chordwise flow would be something like this:



The blue area marks an area of very low-pressure and flow detachment. The outboard wing will experience high pressure due to converging flows1. The wing will want to bend up from the middle, and bend down from the tips, structurally that's a nightmare.

The M wing on the right does resemble birds, but birds had to retain their 'arm' joints from their ancestors, and they don't fly at Mach 0.8 speeds.



1 Answer is a wiki for a reason, this is a guess.