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
No, it's not a bad idea to take out the AT with a TCAS RA. If you get a descend RA with the AT in N1, you will very fast go into an overspeed situation. The AT will remain at N1 in this situation with no speed control.