"The policy rationale for executive privilege is that presidents will not receive candid, unvarnished advice from their aides if that advice becomes public as a result of subpoenas, judicial or legislative."
And indeed, there is some textual support for this in the Supreme Court judgment he cites:
"Human experience teaches that those who expect public dissemination of their remarks may well temper their candor with a concern for appearances and for their own interests to the detriment of the decision making process."
But I'll point out that the Court does not elaborate on this principle much, to the extent that even mentioning it should probably be considered obiter dicta. And indeed, the Court goes on to diminish the relevance of that principle in context:
"However, when the privilege depends solely on the broad, undifferentiated claim of public interest in the confidentiality of such conversations, a confrontation with other values arises. Absent a claim of need to protect military, diplomatic, or sensitive national security secrets, we find it difficult to accept the argument that even the very important interest in confidentiality of Presidential communications is significantly diminished by production of such material for in camera inspection with all the protection that a district court will be obliged to provide."
In other words, yeah, confidentiality is good and all, but it's not enough by itself to override the legitimate interest of the court in deciding whether or not the claim of privilege is legitimate. Courts often do this: acknowledging the existence of a concern or argument without delving into its validity because they consider it irrelevant to the case at hand. (This heads off future objections that the Court failed to consider it. Not as much of an issue at the Supreme Court, from which there is no appeal, but it's still good judicial practice to cover all the bases.)
And because the issue was only raised cursorily for the purpose of dismissing it, the Court did not go into any kind of depth in analyzing that basis of privilege, which is a shame because I think if they had seriously considered this basis of privilege, they would have phrased the description of it quite differently. The notion of executive privilege here is, after all, closely analogous to attorney-client privilege, and exists for very similar reasons. Importantly, that privilege belongs to the client, and emphatically not to the lawyer. And here's why.
We want people to seek out legal advice, so that they can conduct themselves in a lawful manner. The example I like to use is of someone considering whether or not to murder their rich uncle so they can inherit his estate. If they consult a competent lawyer, they will be told "No, that's a crime. You can't lawfully do that, and moreover, there is a longstanding common law principle that you cannot inherit from someone you've murdered, so even after you've served your sentence for the crime you will not receive any money for it." And, presumably, having had proper legal advice, they will know that this is not an option. So if the uncle then dies in suspicious circumstances, the fact that the nephew or niece might have received legal advice on this very subject should not be used as evidence against them.
The privilege does not exist to protect the lawyer. Yes, of course, it is very important that the lawyer be able to give candid advice and not worry about being embarrassed, but there is something seriously wrong if a lawyer gives advice about which she would be embarrassed if it became public. About the only circumstance I can imagine in which a lawyer should be embarrassed by the advice she gave in private would be if it were bad advice, that is, unethical or incompetent. And she absolutely ought to be afraid of giving such advice, whether or not it is revealed to the public!
The same principle applies to advisors to the President, though obviously the scope of what constitutes good or bad advice may differ somewhat. But we can see clearly why the privilege belongs to the President and not the advisor through a simple example: suppose an advisor just straight up offers a hefty bribe to the President as an inducement to make some executive order. Should the advisor be able to rely on executive privilege to shield such an offer from scrutiny? Or would the President be within their rights to fire the advisor and refer the matter to the Justice Department for prosecution? I would hope it's pretty obvious that I favour the latter answer.
So my reading of the SCOTUS remark on executive privilege is that while there might be legitimate military, diplomatic or other national concerns supporting a claim of executive privilege, the idea that privilege must be protected to save the President's advisors from potential embarrassment has no real legal weight. It is the responsibility of the President to select and earn the trust of advisors who will to give him that candid unvarnished advice, knowing full well that same President has the power to make that advice public.