None of her children ever had the Prince or Princess title as none were ever destined to rule.
Indeed. There's a slight difference in form, but the spirit of the change is the same and as you point out, is completely relevant.
The Letters Patent 1864 and 1917 didn't allow for Margaret's or Elizabeth's children to have a title (although that was down to titles only passing down the male line) because they weren't male. If Elizabeth and Margaret had been male, however, both of their children would have been 'Prince/Princess' at birth (which was the rule under the LP 1864 and unchanged by the LP 1917). George VI released a new Letters Patent 1948 around the time of Charles' birth in order to formally recognise Elizabeth as his heir presumptive by granting her children titles at birth. If he hadn't, Charles would have been 'Lord Charles' until Elizabeth ascended the throne.
What the King didn't do is actively prevent Margaret's children from receiving titles they were entitled to already (which would be the case if Charles prevents Archie and his sibling(s) from gaining a title at the point he ascends the throne, hence the slight difference if what was said about him 'never being a Prince' is true). Margaret's were never entitled to one to begin with, and evidently, it was never seen as something to be changed.
However, the effect is the same in practice; only the children of the sovereign, and the direct line of the sovereign's heir, get the title, while the lines of the other children of the sovereign, don't. It's just taken some time and work arounds to make it all work properly as the Letters Patent have been reactive to specific situations. To that end, Beatrice and Eugenie were pretty much just born at the 'right' time to a male son of the sovereign in between changes to the rules. A generation later and I doubt they'd have been entitled to 'Princess' either because they'd have been caught in Charles' slimming down exercise.
It's all very interesting academically at least I think it is.