Checked In on time? You can still be 'too late'.
At least one of the major US airlines (Delta) used to sell or reallocate the seats of passengers who didn't turn up at the gate within 15 minutes of departure (irrespective of whether boarding had been actually been completed).
They also used to fly with the resulting unaccompanied luggage, rather than take it off.
SO; Read your terms and conditions very carefully! Including clauses about punctuality at the gate. Anything displayed or not displayed on the airport info screens is immaterial. The gate clause allows them to give your seat away even if the info screens have not shown your flight to be 'boarding'.