You didn't listen to the oral arguments before the Supreme Court - too bad, although
you can still go back and hear (or read the transcript). Yes, one of the questions asked was that if the president, any president, as president ordered the assassination of the president's political rival, would that be protected as a presidential act (approximately starting at 5:47 again at 19:09). This also appeared in the dissenting opinion.
SCOTUS ruling on Trump vs the United States. The dissenting opinions are worth reading.
From Sotomayer's dissent (pg 96-97) [emphasis added]:
Looking beyond the fate of this particular prosecution, the long-term consequences of today’s decision are stark. The Court effectively creates a law-free zone around the President, upsetting the status quo that has existed since the Founding. This new official-acts immunity now “lies about like a loaded weapon” for any President that wishes to place his own interests, his own political survival, or his own financial gain, above the interests of the Nation. Korematsu v. United States, 323 U. S. 214, 246 (1944) (Jackson, J., dissenting). The President of the United States is the most powerful person in the country, and possibly the world. When he uses his official powers in any way, under the majority’s reasoning, he now will be insulated from criminal prosecution. Orders the Navy’s Seal Team 6 to assassinate a political rival? Immune. Organizes a military
coup to hold onto power? Immune. Takes a bribe in exchange for a pardon? Immune. Immune, immune, immune.
Let the President violate the law, let him exploit the trappings of his office for personal gain, let him use his official power for evil ends. Because if he knew that he may one day face liability for breaking the law, he might not be as bold and fearless as we would like him to be. That is the majority’s message today.
Even if these nightmare scenarios never play out, and I pray they never do, the damage has been done. The relationship between the President and the people he serves has shifted irrevocably. In every use of official power, the President is now a king above the law.