Whilst I agree the translator sould technically be "invisible", fundamentally, the translator will always be felt and heard. However, even the best translation inevitably changes meaning, because even basic words have meanings and connotations in one language that will not, even cannot, accurately survive translation. But it's probably worse than that.
As a simple idea, how you translate idiom? Puns? There is a valid question here, does a translator leave the literal meaning even though the idiom is unrecognisable, or does the translator use an equivalent from their own language? What about slang? Should it be translated formally, or with a sort of phoenetic imitation of the original slang, or replaced with equivalent slang from the country the translation is for? All are defensible choices, but will produce different pieces. If someone writes with the tone of a 22-year-old full of modish street and internet slang, is a stuffy, bookish, 60-year-old translator really going to have the same natural feel for that sort of thing? Arguably not. Consequently, there really is an argument that finding someone with a similar outlook and experience may achieve a better end result.