I know that. When talking about language and script transmission it makes more sense in my view to talk about Phoenicians rather than Carthaginians, unless there is any specific linguistic difference such as dialect that needs to be taken into account (and in this case I don't think there is any such detail). It seems like an assumption not based on fact to assume transmission via Carthage rather than other routes.

Carthage is much, much closer to Denmark, by sea, than Tyre. That matters because theirs was a maritime empire. If there are any differences between letterforms used in Tyre and later in Carthage, the ones from Carthage are the natural choice to check. You could check the others, too, if you liked.