It is not impossible to sue the SEC. SEC suits have been successfully achieved in the past. so it is not absolutely true to forget suing the SEC.
Here is one successful law suit that named the SEC as a defendent:
but note that it took 3 years.
Because the SEC is the regulatory agency, who it self has a purpose of enforcement and litigating against violators, it becomes a large empediment for an individual to bring lawsuits against them.
It would be 95% impossible to successfully litigate this yourself, so you would need an attorney who is heavily resourced, as it will be expensive to proceed and maintain the law suit, until you are able to win. A law suit against this agency will take years, and be very expensive.
Finding an attorney will be hard, unless you have a strong case that promises a return on the attorney's or the lawfirms time; such that they can take it on contingency.
You can add the SEC to the lawsuits currently in progress as co defendents. But that may be a tactical error, because the SEC is an ominous defendent; and when you add them, you now bring a co-defendent to the table with the brokerages, and will make overall litigation of those cases harder, because now the defence would be resourced in part by the SEC.