Errol I'd say that's true that it persists in more insular organisations.
IMO it's definitely endemic in older, smaller firms (I think a PP has said the same) which tend to be more insular and 'old school'. It's also used more in litigation. It's a bit like excessive legalese. People do it because 'that's what lawyers are expected to sound like'.
Bigger firms (IME) tend to prefer a more plain English approach, at least on the non-contentious matters. When you're working on a multi-million pound tech deal, the client doesn't have time to sit and interpret what you're saying. They just want to know what the risk is and what you think they should do to avoid it. Likewise, if you're negotiating with the other side (whether or not they are based in the UK) for the most part you both want it to be as painless as possible, so simplicity is key. Using unnecessarily long words and formalities like 'Dear Sirs' normally (though not always) suggests you're in for a bit more of a fight because it immediately puts barriers up.
Litigious correspondence on the other hand is generally more prone to verbosity, pomp, and bluster (sometimes it's tactical, sometimes it's just stylistic and has been passed down through generations of lawyers). You're more likely to see 'Dear Sirs' from a litigator I think. It adds that extra layer of gravitas (in theory) which most non-litigious correspondence really doesn't merit. I don't like the phrase at all, but I am a bit more forgiving with its use in that context. I don't think it's right and I'm glad firms are moving away from it, but I think it'll take longer for it to go away simply because it's still so ingrained and some trainees are still being taught to use it by people (mostly men) that started practising decades ago when it was a market expectation, because heaven forbid there be a female partner.
Using it outside of the legal market, especially in this day and age, just seems absolutely bizarre to me.