One thing I don't like about this mechanism is that my user would have to go through the dialogs required for each one of my in-app purchases and buy the free-trial version of each. Why can't I just keep up with the original purchase (download date) of my app, let them use all the features of the app for free, then after the 14 days, start requiring a purchase for the premium features?

One thing I don't like about this mechanism is that my user would have to go through the dialogs required for each one of my in-app purchases and buy the free-trial version of each. Why can't I just keep up with the original purchase (download date) of my app, let them use all the features of the app for free, then after the 14 days, start requiring a purchase for the premium features in order to continue using them? You could display a custom "you are beginning a 14-day free trial of this apps premium features" to make your users aware this way they don't have to take any action on their part to start the trial.