For starters, was it really a tragic inevitable destiny? From what I understand, it's all Montague's fault for wrecking the balance that kept Neo Verona aloft, and he's the one that killed all of the Capulets except for Juliet.
Sure, the finale and the supernatural villain are not uncommon to fantasy anime. Still, it wasn't entirely out of nowhere, since the show kept showing her throughout the series and eventually started showing the decay that was clearly going on.
If this weren't Romeo and Juliet, the series could have been made to end with Montague's death and it would have been fine. However, it was, and one has to wonder what the reaction would be if it had ended there. Then the show risks a feeling of "oh, they made up a standard happy ending out of nowhere." And while that'd be satisfying in and of itself, it would have become completely separate from Shakespeare's story.
Not to mention that the deaths, while tragic, are preferable to the pointless deaths they suffered in the play. Given the way the story of the anime played out, copying the play would have felt extremely forced. For instance you get the sense that if anime Romeo had survived whereas Juliet did not, he would have grieved but he also would have gone on to be a good ruler.