I think that was an issue of it's time, in that when Carr was down, the team didn't want to make Taysom and Haener the back ups behind Winston, because if they did, they'd be restricted in how they used them during the game by the emergency QB rule. If they wanted Taysom to be able to play his non-QB role, I suspect they also wanted a more experienced QB behind Winston.
With Carr back, things return to normal and the Di Nucci option fades as a beneficial one.