Cadets and Ensigns would not be given command of a ship, and everyone in STO will have their own ship. It makes perfect sense to start as a Lt.
Starting as a Cadet at the academy would provide the perfect environment for a tutorial. Most of the training can happen though Holodeck simulations.
Upon graduation, your first assignment could be aboard a station where you are often sent on an array of missions using the station runabouts. You don't absolutely have to have your own ship the very first minute of gaming to make it interesting. As a matter of fact, it's my opinion that this will ruin the experience for me.
The Star Trek Experience should be started from the beginning, not the end of your career.