The point was that I disagree with TPTB making her invent something rather than having her simply speak more clearly for the Yanks.
Then why make her a half Betazoid?
Why put pointed ears on Spock?
That analogy doesn't work at all! Creating halfbreeds is relevant to the story and to character development. Being half human defines Spock's character, as does his Vulcan appearance. The same goes for Troi and her empathic abilities instead of telepathic.
Her accent is completely irrelevant and the fact that she mumbles about in something that no-one else even tries to imitate has nothing, nothing to do with the fact that she is half Betazoid.
Give me an example of why on Earth her weird mumbling is supposed to better the character, and I might concede the point. As it is, I stick with my opinion: either have more Betazoids talk that way, or leave it. Say it was the universal translator, or better, don't comment on it (as was the case with Spock's dad in ST09). She can speak more clearly to accomodate the Americans, but don't make up some "accent" that is not native of anything and doesn't do anything for either story or character development. It would have worked if it had been an issue, but since everyone ignores it, nobody talks like that and it's generally a big fat no never mind....don't bother.
Stephen King says that you must kill your darlings, which means cutting out stuff that doesn't matter for anything. Face it: the accent was utterly useless.
And again: why is it a problem to have several people on the bridge being from England? Apart from the fact that there are several different accents in England alone (not taking into account the rest of the UK and Ireland), all they need to do is follow the American actors' example and speak clearly.
On a different note, I find it funny that Cumberbatch is bored of denying his character is Khan. I still believe he won't be, but I can understand where he's coming from.