I am writing this for those who aren't aware of how Trenitalia's seating system works. I made errors. Some due in part to forgetfulness, others due to ignorance and lack of information available. Hence this post.
If you are traveling on a Fecciarosa train, purchased a ticket through Trenitalia's website, and forget to select the option to select a seat, you are not left to the wolves to find a seat when you arrive. You will be assigned a seat by Trenitalia at the time of purchase. It may or may not be exactly where you would want to be, but you will have a seat. The "select a seat" option is simply to select the exact seat you want, for a small fee.
I looked this situation up for several hours online and no where, including this site, did it state that if I didn't choose my seats a seat would be assigned to me. Hopefully others can learn from my stupidity and not feel as if you have to consider purchasing a ticket a second time, just to finally reserve a seat. Before anyone points out the obvious stupidity of this situation, there are extenuating circumstances that provide a bit of context as to the need for reserved seats.
Marc