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SIPC (Securities Investor Protection Corporation) protects your assets in a brokerage account in case your broker goes bankrupt. Note that it does not cover investment losses (for example if the stock market goes down), but it does protect you in case of a broker's bankruptcy.
Not to say that if your brokerage goes bankrupt, it wouldn't take a while to get your money. Just like if your bank with FDIC insurance goes belly up, it may take a while to get your money back. So for this reason, I can see the desire to split your savings between multiple banks. However, your brokerage assets should be your longer-term savings anyway, so I don't see a real need to have more than one brokerage.