In a recent post, Professor Stephen Bainbridge expounds on the question of whether the President may fire Chairman Gary Gensler. He concludes:

I am not "really sure" Gensler can be removed from his position as SEC chair. But I am pretty sure at about a 95% confidence level. It has never been done, but as I explained in the original post the consensus view (that I share) is that the Chair serves as such at the pleasure of the president.

Professor Bainbridge focuses his analysis on three old Supreme Court decisions - Myers v. United States, 272 U.S. 52 (1926); Humphrey's Executor v. United States, 295 U.S. 602 (1935); and Wiener v. United States, 357 U.S. 349 (1958). When I addressed the same question about seven years ago, I focused on whether the Securities and Exchange Commission is truly an "independent agency". 

More recently, the Supreme Court held that the Sarbanes-Oxley Act's dual for-cause limitations on removal of members of Public Company Accounting Oversight Board violated the U.S. Constitution's separation of powers. Free Enter. Fund v. Pub. Co. Acct. Oversight Bd., 561 U.S. 477 (2010). In that case, the Court proceeded with the understanding standing that "the [SEC] Commissioners cannot themselves be removed by the President except under the Humphrey's Executor standard of 'inefficiency, neglect of duty, or malfeasance in office'".