I believe the way out of 1929 was to print debt free money into the economy to counterbalance the decrease in loans.. to write off a huge amount of debt by allowing big bankruptcies.. thus keeping that money in the system.
Likewise in this situation I don’t think its a great idea to try to continue a great wave of new borrowing by lowering interest rates to nothing. Thats what they did in 2001.
I think you've got your years mixed up. Had Greenspan not hiked rates too high, and been so slow to correct his mistake, then rates never would have been lowered to 1%.
In our current situation, the damage has already been done. Lowering rates now isn't going to change that. The longer the Fed waits, the more it's going to have to lower rates in the future. It's like the mechanic says, you can pay me now or you can pay me later.