A competent pilot should have noticed their airspeed was inadequate WAY before the boundary fence. A competent and alert pilot should have noticed inadequate airspeed before the plane covered a quarter of the runway and either hit max throttle or abort takeoff before reaching a critical point.
The only problem with aborting is that the abort speed is predicated on several factors, one of which is weight. If you are not accelerating as fast as you should be you will reach your computed abort speed further down the runway leaving less room (and possibly not enough room) to accomplish the abort. You’re absolutely right about pushing up the power though. Once the end of the runway was coming up and you’re still not airborne the only real option is to push up the power.