Very few names fall out of fashion permanently. If you'd have told people in 1990 that Arthur would be the most popular boys' name in 2021 they'd have laughed in your face
Many many names fall into obscurity, some never to be heard of again. Take many of the names from history or classic novels, did they all go through a revival? Or just vanish? How often do you hear of a baby Estlethwaite these days? Or a baby Prudence?
Arthur was always going to have links to King Arthur and mythology so I don’t think it’s a surprise it came back into fashion?
Names that were popular over a century ago seem to have a different reception when revived eg Biblical names, certain Latin names, many names connected to royalty or intertwined with history. For example Horatio makes people think of the famous French Admiral Horatio Nelson whose statue still stands in tourist spots?
Names from Shakespeare; some have remained popular (eg Miranda, Juliette, Lysander) others fallen into near obscurity (eg Hermia, Prospero, Oberon etc).
To me Brian is similar to names like Colin, Simon, Wayne, Barbara, Dennis, Sharon, Beryl, Joy, Leslie, Walter etc. Maybe I’m wrong and it’s from a different era but it feels like a name from that time period somehow.
Of course I could be wrong and it could make a comeback one day! I just don’t think that time has come yet, especially with the unfortunate character in the infamous comic satire movie which is probably why your MIL gets the giggles?