The recent posts here are making me think of a few instances that came up in a drama I watch in which many characters are Deaf.
One instance shown in how hearing people being able to sign would be incredibly useful is in hospitals. In the show a couple of Deaf people get into an accident and no one at the hospital tells them anything. They get patched up, but no one will tell either of them where the other is, nor any information on what has actually happened to them. They can obviously work out if their arm is broken due to whether they've had a cast put on etc., but they haven't been told about it.
You could say that the NHS should provide keyboards for Deaf patients, but the NHS doesn't have enough money as it is and the computers can be incredibly slow anyway. You could say that BSL should be part of the training to become a nurse, doctor or NHS receptionist, but as you've said learning a language from a young age works best... like learning it in schools.
There are many jobs where it at least could come in handy to know it. Teacher, lawyer, policeman, fire-fighter, barista, shop clerk, tailor... the list goes on. Knowing BSL helps let Deaf people know that the hearing world still considers them as part of the country and that we still believe they matter.
Also in the show I mentioned before a Deaf character was deeply struggling with an essay. He understood everything about it but his grammar was terrible. He pointed out how in English there are so many versions of a word; see; saw; have seen; will see; while in sign language it's just one sign. Sometimes it's still easy enough to work out what the person means when (s)he says something like "I saw what you mean", but there have been times when even hearing people, whose native language is English, have messaged me something that I couldn't understand in the slightest. If people who have known it their whole lives can't always make sense with it, how can you expect every person in a group who likely have it as their second language to make sense with it?
Also if by the interpreters dominating the court case you meant it was taking so much longer there are two things I wish to say on that subject.
1) giving them all keyboards could easily take longer even if everyone involved is 100% fluent in written English - have you seen how slow some people type?
2) it could have been solved by everyone involved knowing BSL.