Sagrada Familia may be an unhappy travesty, but every cathedral is, and few have such a consistent style. Even our cities are unhappy travesties, and I do not think that leaving the unfinished works of deceased architects unfinished would change that.
You have all the right to dislike how it is being done, and it may be not exactly what Gaudí thought, but trying to finish it was, in my opinion, the right decision. When you are in the middle of a task that will take generations, it makes sense trying to continue even if some accident happens, like your main architect getting killed by a tram or documents getting lost.
> every cathedral is
Actually, contemporary cathedrals (of which more than a few have been built in the XXth and XXIst centuries) are typically completed in a reasonable timeframe. 5 years for Moneo's Our Lady of the Angels; 3 years for Hartman's Cathedral of Christ the Light, and so on.
By the way, the Sagrada Família is not a cathedral, but a basilica, but that is neither here nor there :)