>There is a mechanism for prosecuting presidents, impeachment and a trial in the Senate
That is not a substitute for prosecution, it is a political process for removing a president. The Constitution's authors likely meant it to be used when a president ignored their duty, violated the Constitution, or lost public support before the end of their term. These are not federal crimes, so they don't go through the federal courts. The impeachment and removal process does imitate indictment and trial, but that's because there's no reason to reinvent the wheel.
The SCOTUS ruling went far beyond historical practice. Historically, officials weren't prosecuted for official acts unless it was shown the act was part of another crime. So if the President delayed a FEMA response because of budget worries or incorrect forecasts, nobody would be prosecuted or open to lawsuits from citizens who suffered. But now, no official investigator can interview an appointed official to find out if the act was done as part of a crime. Worse, if the act was a presidential power enumerated in the Constitution, there is almost no way to investigate its use in an obvious crime. If the President only pardons people after they pay him $20,000 dollars, the President is immune from investigation.
A hypothetical raised in the dissent is still an open question: what could be done if Donald Trump orders a military strike team to kill the next Democratic presidential nominee? Do you expect this Congress to actually impeach him? After he lied to, riled up, directed, and have plenty of time to a mob who invaded Congress and built a gallows to hang the Vice President? And Congress didn't prevent him from ever holding office again?
I am not swayed by any argument along the lines of "But the President will be too worried about vindictive prosecution to make the right choices." If we really need to prevent that, I'd rather have every president thrown in prison for life after their term. No need to worry about prosecution, because you already know what awaits you. The office is more important than any individual holding it.