> I wonder to what extent the overarching business culture of the UK (which I'd categorise as being generally apathetical, if not hostile, to the engineering profession) might have anything to do with it.

That's nothing to do with it - the company is only listing on NASDAQ - ARM has office all over the world but will still be based and managed in the UK along with most of its employees (engineers) like when it was owned by a Japanese company.

Listing on the tech heavy NASDAQ rather than the LSE gives the company more access to investors that are likely to buy shares: retail, commercial, and hundreds of index trackers and funds - increasing the share price.