If it is you that has a connecting flight (a change of planes) then you will get two boarding passes one for each flight. The EBCI will give you an advantage on the first leg and you will be able to get both boarding passes with EBCI.
If you are flying on a flight that is a connecting flight for other passengers, the connecting passengers will also have two separate boarding passes but they will have had an advantage of being able to check in at T24 of their first leg for both flights. In this situation I see EBCI as being advantageous as you will get your BP before non EBCI connecting to your flight.
If you are boarding the second leg of a continuing flight (passengers continue on the same aircraft without deplaning) they will already be on board and will have the best selection of seats. I also see EBCI as an advantage here, not over the continuing passengers but over the non EBCI passengers on your flight.
If you are only uisng EBCI to get exit row or bulkhead type seats then you are right they will most likely be taken and it may not be worth if if you are all adults. However, if sitting with your party is important I would still get EBCI regardless of continuing passengers.