There would be no point if you were to take only a two point average from the start and end times, because they are common between successive intervals. Fair enough?
Good point in this case, since it is only the cumulative total that we are interested in.
In the more general case, a simple addition gives inaccurate interim results so that using it for double integration (accel/speed/distance) could produce substantially inaccurate results. That doesn't apply here, though, and you're right that simple addition is all that is required (except for a little fudging at the ends). Personally I'd use the average anyway, simply because I'm used to seeing it and so it looks right to me, without needing any special handling of boundary conditions.