Is it important to diversify by holding investments with multiple investment management firms?

No, that serves no purpose. The security you invest is only held by the broker in kind or in you name. If they go bankrupt, your security is safe because the broker had no stake in the investment but facilitated the sell. If you are happy with your investment strategy, just buy ets from one firm, preferably with the cheapest trades! BofA Direct Investor has $7 trades if you meet certain requirements.