If the money market accounts crashed, financial companies wouldn't have been able to roll over their short term debt, which they rely on for day-to-day operations. Non-depository institutions (like the surviving investment banks) would be forced into bankruptcy. Those bankruptcies would cascade, and depository institutions would fail as well, probably with bank runs on accounts over the FDIC limit.
What made the Great Depression great were the banking crises. Without a functioning financial system, a modern economy can't grow. And if we reached a point where people couldn't even get money out of ATMs, we're talking about complete social breakdown. One Congressman claimed the administration talked about martial law as a real possibility. We really did come close to the brink. And the downward cycle went even faster than prescient bears like Nouriel Roubini thought it would.