My answer is NO if you have your account with one of major brokerage and fund companies, like Fidelity, Vanguard, Charles Schwab, etc.
This also depends on individuals. Someone might sleep better at night if he or she has an account each with two different brokerage companies. To someone like that, I would suggest to open accounts with no more than 3 major brokerage houses while he or she has $10M investable asset. Even though, you have accounts with 3 firms, it does not mean that all your money is with them. The reason being is that you buy mutual funds and the money is actually with the mutual fund companies, not with your brokerage companies.