Oracy is an important skill, and helps develop written work - for example, we have kids who can't spell simple words, because they have never heard them spoken properly (they'd automatically write something along the lines of 'cos they'ind herd'um proply', for example).
We don't award GCSEs in other languages without assessing ability to speak the language and being able to hear how something is phrased, the rhythms, the consonant sounds, the stops, give a far greater understanding of rhythm, rhyme, pentameter, tone, punctuation, syntax, grammar and content; all essential for being able to write clearly, persuasively and creatively.
In addition, developing Oracy skills doesn't just give greater confidence, it affects the way people are perceived - for example, if you are interviewing a mumbling teenager with a strong accent and use of slang terminology as associated with Grime music that some will assume to be Gang Culture and one who speaks clearly and confidently, it's unlikely to be the first teenager who gets offered the job that requires speaking to clients. (Yes, I know there's an element of racism in that decision, but the same applies for any strong regional accent)
It also encourages attention to detail and benefits other subjects such as Music.
I grew up with a very strong local accent. However, as I read more (which improved my vocabulary dramatically, as home was not a place where long words were spoken - they were derided), my accent changed. I was told I sounded like my deceased grandmother [shrug]. The result of that was I had a speaking voice that got me jobs involving high level client contact - fairly or unfairly, people who are most likely to be in positions of authority tend to associate poor oracy with lower intelligence. A kinder way of putting it might be that Oracy skills give the impression that somebody is better educated.
I normally wonder what private schools do when a particular idea is discussed, as if something works, the odds are that they do it for their students first/have been doing it for years.
Private schools do have lessons in Oracy - it helps their students progress, even when they are not high achievers academically and whether they have a strong accent from in or outside the UK.
Moreover, it's been tested as part of the English Language GCSE for at least thirty years, so they aren't about to stop now.