You keep asserting this, but it isn't true. There are contemporary accounts. They just don't support what you want. For example, the De Excidio Britanniae had plenty to say about the ravening hordes of Saxon invaders causing destruction and famine. It was written (another example of those darn illiterates still stubbornly producing writing) in the 6th c., contemporaneously with the historical Battle of Badon Hill of Arthurian legend.
Yet, despite his obvious relish at describing the horrors of the Saxon invasion, Gildas makes no reference to a climatological catastrophe.
Later, Medieval cities were frequently sited in the same areas as earlier Gaulish and Roman cities and towns.
Yeah. Because they never stopped being occupied. Rome dwindled in size because it dwindled in importance following the Eastern Roman Empire and Byzantium, but it was never abandoned, even after being sacked. Paris, OTOH, grew. So did Aachen and Cologne.
They are not, BTW, legends ~ just that you don't know what the Breton word for Arthur is, nor it's historical use ~ try Boadicea, which is both the name of a British revolutionary in Roman times, and a sentence. "Bo" means the same as "Mc", or Abu in Semetic languages ~ that is, paterfamilias. "a" or "ad" is "Arthur" or "military leader". "dic" (with a hard c) is a fairly universal term meaning "king", "lord", "ruler", etc, but here it's feminine in form suggesting we are talking about a great queen.
So, there's your "Arthur". How it got preserved down to the 6th century (538/540) is a real good question.
BTW, both of the aforementioned documents were mostly written BEFORE 540, and that Excidio contains few real dates!