Its been a long time since I worked on the 737-200. Something tells my overused memory that the physical arrangement of the pneumatic components was such that the bleed valve had to be open to allow air to the start valve. When the -3/4/500 was launched, even though the engine pneumatic arrangement is different the SOPS were left the same for starting the engines just to make transition from old a/c to new simpler.
But I could be wrong.
Also, I'm pretty sure the CFM56 has surge bleed valves aft of the booster stage, automatically controlled of course.