Usually, a trust would avoid the need to probate the estate. It sounds like your father has already done that by titling everything in your name. As you have described it, upon your father's passing, there will be nothing to be done other than possibly a summary administration if there is any miscellaneous property that needs to be devised.
There may be a benefit with taxes and for protecting the assets. You may want to consult a tax attorney, which I am not. It's not clear what you may want to protect the assets from, but you may want to speak to an estate planning attorney about that.
A trust can help protect against unforeseen issues, such as you dying before you father, which would cause the brokerage account to go through probate. A trust could also be structured to avoid estate taxes at your death as well, and probate the assets from your creditors. Trusts are much more flexible and protective than TOD and other methods of transferring property.
Whether or not a trust is needed depends a lot on the value of the remaining assets to the estate. If your father's attorney has advised him not to bother, then he probably is more aware of the nature of the estate and assets than any of us on this forum could be. Assuming your father is happy with his attorney's advice, he should listen to it.
Carol Johnson Law Firm, P.A. : (727) 647-6645 : firstname.lastname@example.org : Wills, Trusts, Real Property, Probate, Special Needs: Information provided here is anecdotal and should not be relied upon or considered legal advice. Every matter is different and answers given here are general in nature and may not reflect current Florida law at the time you are reading this posting. Please contact me if you feel you need additional assistance with your matter.