How will you know that the flight is full?

Even if it was, you can never assume that checking in at the very last opportunity that the situation has not changed. This is the most fluid/flexible time - if an incoming flight is delayed, the computer can automatically offload the pax that already hold boarding passes for your flight, and suddenly there are loads of economy seats available for you to select from.

And you can never be sure that you will be the very, very last person to check in - and letting it go that late means you risk missing the check-in deadline yourself!

If there's even just one empty economy seat unclaimed when you check in, then you will be stuck with a middle seat, probably at the very back of the plane.