Makes sense to me.
Something that occurred to me is that until the Twety-fifth the consitution doesn't name specifically any department, how many there would be, the composition of them, just that there would be departments and the President is required to get the opinion of the principal officer of said departments.
Maybe one small difference the Consitution would name the departments there would be instead of being establish through Congress their and establish the order in which the succession takes place.
Constitutionally speaking, I don't think there is any stopping the President from making cabinet system more akin to the system to that of UK or Canada. I think the advisory-cabinet style is style the they would have choose as it seems to me that's the more powerful executive option. I would argue that it's also against the idea of separation of powers, but that doesn't make it illegal.
Here's a wild idea would the consitution be silent on succession who succedes ? Perhaps, in this scenario the original consitution would be just as silent on succession beyond authorizing Congress to develop a succession.In our timeline, the unamended Consitution just names VP. Maybe Congress goes back and forth with fighting over who gets maybe in a few decades. The Cabinet are successors for a time. Then the President of Senate takes it for a few decades, then maybe Speaker House takes for a few decades.
