There is some rationale to having an Acting President in the case of a President who is (possibly temporarily) incapacitated, but none if the office is vacant due to death or resignation. Given that such a case has never actually occurred, the apparent conflict between the Presidential Succession Act and the 25th Amendment would need to be resolved by the Supreme Court.
In any case, you can’t argue that an Acting President must have all the powers of the President, because “otherwise the concept would be pointless,” while at the same time arguing that an Acting President would be replaced by an appointed Vice President, because that would also be pointless. You can argue either that the text of the laws should be taken absolutely literally (in which an Acting President doesn’t have many of the powers explicitly specified for a President); or that common sense should govern their interpretation (in which an appointed Vice President would not replace an Acting President); but you can’t argue one way in one case and another in the other.
I disagree, except for very limited circumstances.
There are two possible scenarios, one in which the President is alive but temporarily incapacitated and the other in which the President is dead or otherwise permanently incapable of office.
“In case of the removal of the President from office or of his death or resignation, the Vice President shall become President.” That’s from the 25th Amendment, which settled the 200-year-old question of whether the VP becomes President or is Acting as President after the death of the President. Whatever “Acting” means. In the eight cases of presidential death before that, the new President was treated, de facto and de jure, as the President. There still was no solid foundation for doing so. The purpose of the 25th Amendment was to correct that. Today it is agreed that whoever becomes President upon the death or removal or permanent incapability of those above in the order of precedence is the President, full stop. Interestingly, it is still debated whether this happens immediately upon death or when the new President is sworn or affirms in. Again, nobody has thought to put this into law.
If both the President and VP die simultaneously, the Presidential Succession Act of 1947 made everything worse by language that was particularly slippy and, some say, nonconstitutional.
That’s never been tested in real life and so is a Schrodinger’s Cat of law, with dual meanings until one is settled upon. All other law treats the succession as real, however.
The powers and the office are therefore separable only if two candidates for the position are alive, as in Section 4 of the 25th Amendment. The could be the Pres and the VP as in the few times its been invoked, but it could equally be the Pres and someone farther down the chain. That state can only last up to 21 days. At the end of that time, one of the two becomes the President.
But none of that can come into play with a dead President. If only one legal candidate is alive, that person is the President and has both the office and the powers.