Minderwiz
Did Alexander the Great's astrologer rotate his chart before electing when to conquer the next territory?
No he didn't, Not once!.
The reason is that natal charts in the sense of being based on an Ascendant and a house system did not exist till about 300 years after Alexander died.
He might well have taken note of locally observed Astrological phenomena, as good or bad omens.
I've not come across any significant use of relocations until Morin in the seventeenth century and he used it for Solar Returns.
However I don't see this as invalidating the concept of relocation. You mention elections later on in your post and the Astrologer of a late Hellenistic or Medieval Alexander the Great will have used the location of the proposed event, rather than the birth place of the native. The most well known example is John Dee's election chart fot the Coronation of Elizabeth I, but I'm sure this had been standard practice for some centuries.
The real issue though is the one that you raised about the continuing validity of the natal chart when a person moves a significant distance from where they were born on a permanent or semi-permanent basis. That obviously begs a whole series of questions:
What gives a chart validity and how do we assess it?
How long does a person have to move for, before their original chart loses some of its validity?
How crucial are these factors in interpreting a chart(s)?
What is the process of interpreting a chart in relation to a future event. or more simply what is the process of chart interpretation?
We might come to different conclusions on those but I think we would agree that the death of 1,517 people in the Titanic disaster can't be explained solely in relation to their original natal charts; and that the chart for its sinking is a relevant factor.... of would we?