The issue is that nothing's come off the metaphorical chalkboard. Nothing's been erased, that's been made painfully clear since the talk of timelines came up years ago. Everything people assumed had been retconned out, as it turned out, was all still there. Even the stuff that was downright contradictory thanks to their 'official' places on the timeline. Instead what's been happening is they're drawing the image, and constantly taping more paper to it, making it bigger and more confusing as they go.
The concern regarding the timelines, the fact that one time should have stopped... should it? I'm not so sure. Of every concept of time travel you'll find in videogames, comics, TV, the only constant that this series keeps up is that time doesn't stop. Everything continues, regardless of where Link is within it. Where other time-travel plots will erase whole timelines (in order to prevent paradoxes), this series embraces the idea of paradox, and doesn't mull over it too much (Song of storms, Triforce 'prank'). Another time-travel based plot involves time 'fixing' itself, which also doesn't happen here. Realistically time doesn't stop, no matter what. So why should time stop in a 'doomed' outcome, simply because a protagonist disappeared? If a paradox isn't going to bring a timeline down, I doubt a missing hero will.