The story we got in Destiny was not the story that Bungie's writers had originally planned to release with the game. According to six individuals who claim to have been at Bungie in 2013, everything that had been written by Bungie veteran Joe Staten and his team was scrapped.
Sources reached out to Kotaku to reveal the truth behind the original Destiny plot, saying that the game's story underwent a full reboot a year before release after Bungie reviewed the story's supercut. The entire plot structure in Destiny was reworked, characters were overhauled, a majority of the dialogue was rewritten and certain locations were scrapped, like Oryx's Dreadnaught.
If the sources are accurate, Destiny's original story had players hunting down the warmind Raputin – who in today's Destiny doesn't hold a very prominent role. In this storyline, players would rescue an Exo that turned out to be controlled by Rasputin, but players wouldn't find that out until DLC for the game was released. Osiris would have been a 'mentor' for players, who had a robotic assistant – now known as the Stranger.
Another character that would have appeared in the original game is the Crow, a character that was essentially The Taken King's Cayde-6. At this point, there's no saying whether or not the original story would have been better or worse.
You get what you get.