Really interesting article. The intro and conclusion suggest that there is some sort of debate going on about usage of "Anglo-Saxon", but I cannot work out what it actually is and what side the author is on.
Similar debate has been going on about “Celts” for many years. Broadly labelling cultures is just a helpful method for making sense of a very messy and complex history. It doesn’t necessarily mean they were completely distinct groups of people.
The article basically TLDRs as "Anglo-Saxon" is appropriate, is my take on it: "In an informed view, it is hard to see ‘Anglo-Saxon’ as inappropriate to the contexts to which it has been attached"