For banks, FDIC matters. Keep in mind it is 250k per registration type. That is 250k for your individual accounts, 250k for an IRA, and if you have payable on death accounts it can grow with the number of beneficiaries. When I was in banking I once helped an individual build his FDIC coverage to over 2 million all at one bank.
For SIPC I think it is first important to explain why you need FDIC. You need FDIC because the bank is taking your safe guaranteed money and investing it in things that aren't risk free, like mortgages. This causes a problem. The bank could go under using this model and you lose your safe guaranteed money. FDIC fixes that. Money in a cash account with a broker might have the same problems, but investments don't. When you invest in VTSAX you know it isn't guaranteed, you know it will fluctuate. You are accepting the risk, not the broker. In this case your biggest concern isn't the broker going bankrupt, you just transfer your shares somewhere else. Your biggest concern is that the broker will 'lose' your shares... aka fraud. In addition, brokers money and your money have to be segregated.
Look at VTSAX. Let's say you hold it at Fidelity.
1. It is VTSAX. It isn't a ponzi scheme. It isn't some crazy investment scheme that can go to zero. It is VTSAX. It's roughly 3600 different US companies.
2. If Fidelity goes under you can transfer VTSAX somewhere else, like back to Vanguard. Real life, this happened with Lehman. While a lot of people who invested directly in Lehman lost money people who just held securities there got their securities back.
3. If Vanguard goes under you are still fine. The Vanguard Group is one entity and the mutual funds are each their own investment companies under that umbrella. You could just transfer VTSAX somewhere else. Your biggest concern here is that without Vanguard's backing VTSAX might incur a lot of new costs so the ER could go up. With a fund that big, chances are a company like Fidelity would be happy to take VTSAX under their umbrella.
Another thing to look at, what is the broker's primary business? With Lehman they went under not because of what their brokerage side was doing, but because of what the company was doing in it's own accounts. Is this a risk with Merrill, Goldman, Morgan Stanley, etc.? Sure. Is it is risk with Fidelity or Vanguard? I don't see why. They both specialize in acting as a broker and managing mutual funds. Neither of these activities seem to be the kind of thing that could blow up the company. They could go bankrupt, but more likely because costs start to exceed revenues, and not because they had leveraged holdings in subprime mortgages. If they held anything like that it would probably be within mutual funds where the investors, and not Fidelity/Vanguard, are taking the risk.