I came up with the same conclusion a while back for my projects, BUT it only makes sense if there isn't a feature differentiation between the Free and Paid products. If the Paid products do come with compelling features then it will make a lot of sense to have a Trail period as it will give potential paying customers an opportunity to "test before buying".

Having said that, asking for payment info upfront is generally not a good idea when you have a trail period. But then again, if you do not pick it up, you might get some abusers who won't cough up the dough after the trail period is over.