The ARM mode is a carry over from B757/767 where it is a design feature, I think, unless dementia has crept up on me unannounced. It's been a few years since....
People then went to the B737 MCP and played with the buttons and found that an 'ARM type mode' could be created and it seemed to be providing the same function as on B757/767. So guys started doing it and some CP's found out about that. As they didn't fly too much, and had never flown B757/767 they did not understand it. The normal human reaction of a manager who does not understand something is to ban it, so they did.
They also went to Boeing and asked the question; to back up their banning, and came back with the 'does not recommend' answer. So the ban stayed.
Now that begs the question how it can become an SOP? The manufacturer AND their XAA have to approve a 'non-normal'.
Regarding some comments about safety features and why Boeing would not recommend them: Boeing has this fixed philosophy that manual flight = manual controls + manual thrust. "period." So they changed TCAS RA to disconnect the lot. Previously it was AP only and leave AT in. Good idea. Then the philosophy gurus reviewed this, noticed the discrepancy and instructed AT disconnect. Bad idea. Why disconnect a safety feature? What problem had ever been created during a TCAS RA using AT? If it ain't broke don't fix it. Even if you apply the "what if' risk assessment I can not think of an answer that would cause the AT to be thrown out. When I asked a Boeing TC the reply was the philosophical one. No other reason.
However, they also had no idea about selecting 'TA Only' during an Emergency Descent or any other performance related non-normal incident; only the engine out case. Perhaps their philosophy nerds need some rebooting.