Why do fansubbers and maybe official subs replace onii-chan/onee-chan with the character's name?

Localization. It depends on the fansub group of course, but many subbing groups cater to an English-speaking audience. As a result, a fair number of them decide to use "natural English" (i.e. spoken English that an English-speaker would have no problem reading) instead of leaving in the Japanese cultural aspects of the language. It's also why a lot of groups leave out honorifics in their translations as well.

As Smitty said, "onii-chan" and "onee-chan" aren't English words, and so if someone who knows absolutely zero Japanese read "onii-chan" in a subtitle, it would just confuse them. When it comes to Japanese/English transcription, sub groups usually have to make a choice - whether to preserve the subtleties of the Japanese language and possibly risk confusing the watcher, or ditch them and make it as fluently English as possible.

Of course, there are people on both sides of the coin who support and detest localization of subs. Supports argue that, as English speakers, why should they care about what the Japanese actually is? All they want is to understand what the characters are saying. You shouldn't have to learn Japanese to enjoy watching the series.

Those against localization prefer to keep those aspects of Japanese, citing authenticity reasons, among other factors. They believe that subbers should only translate a Japanese sentence enough to be understood in English and reflect the true Japanese meaning as close as possible. People learning Japanese also tend to dislike localization.

So there have always been those in favor of localization and those against. Sometimes fansub groups who do localization get blasted because of an incorrect or completely different translation than what the character actually says (http://www.crymore.net/category/fansub-review/ loves doing this). Sometimes fansub groups who don't do localization are mocked because their translations are unnatural or silly (e.g. Light's famous "All according to keikaku. [T/N: keikaku means 'plan']").

So yeah, kind of a long answer, but localization is essentially why.

Because onii-chan and onee-chan aren't English words. In English you use your sibling's name when talking to them.

It's to avoid possible negative attention that the show would get in the west because of the incestual content of the show.