MBAV is a milspec armor cut. If you are in the military, you have to wear issued armor or risk getting chewed out, and worse, your death-benefits might not pay out if you get hit while negligently NOT wearing your PPE.
For a long time (and probably still today in some types of ops) the standard armor package for SOCOM was BALCS armor, a full cut, 360 wrap around soft armor package that was a little more lean than the IBA/OTV/IOTV in use by the standard army or the USMC equivalent, plus SAPI plates in front.
Due to lessons learned in afghanistan, plate carriers became popular, different threats and all. They needed a standard plate carrier armor package.
At the time Eagle Industries Plate carrier's were part of the LCS bags. The MBAV armor was essentially designed to be compatible with the MLCS/RLCS/SFLCS Eagle plate carrier. That's why they are shaped funny. To fill the voids in the then standard issue plate carrier for maximum frag coverage.
Fast forward to today, MBAV is what's in the system, MBAV is what they have to wear; MBAV cut PC's are made by numerous companies today.
There are also a few other cuts that exist in use today like the "concealable" cut paraclete and velocity system soft armor packages.