You can omit columns on a per-row basis with the DEFAULT keyword, it's just more cumbersome if your rows are very sparse. Your proposed syntax of:

  INSERT ... VALUES (C1=v1, C2=v2), (C3=v3, C4=v4), (C5=v5, C6=v6)

in standard SQL is

  INSERT ... (C1, C2, ... C6) VALUES (v1, v2, DEFAULT, DEFAULT, DEFAULT, DEFAULT), (DEFAULT, DEFAULT, v3, v4, DEFAULT, DEFAULT), ...