Originally Posted by JohnBurke

No, they wouldn't eventually have flown, unless they had unlimited runway. The rate at which the airplane increases velocity will not be the same at a rotation attitude, vs. driving down the runway with the nosewheel still on the tarmac. It's quite possible to use up the entire runway in a rotation attitude and not reach flying speed. Now much and how far, really depends on how great the error, the amount of runway, conditions, weight, etc. There is no guarantee that they'll climb away from the runway in the rotation attitude.

If the airplane isn't climbing in the rotation attitude, increasing attitude isn't a good idea, nor necessarily one which will achieve flight, setting aside the damage from the tail strike.

Boeing prescribes maximum rotation angles, above which a tailstrike will occur, and provides them for compressed and extended struts; the maximum angle to which we should rotate prior to leaving the ground is not a mystery; it varies with the specific model aircraft (and length), but it's not an unknown value.

Hold max pitch and go off the end at takeoff thrust is an idiotic idea. We don't want to go off the end. That does raise the notion of what constitutes takeoff thrust. If we know max blast for the runway and we know we're using a reduced thrust/assumed temperature value, then we're not limited to reduced thrust any more than we would be in a windshear encounter. So, increasing thrust may be an option, depending on what the TOLD data is. If the takeoff weight in this case was calculated thirty grand under, and thrust was prescribed accordingly, there's a good chance that additional thrust may be available.

If the airplane isn't flying and we're past. VR, which we will be if we began rotation at VR, then as you note, we're past V1, but we're also in a state in which the airplane is not flying. This might be a tie to consider Air Florida 90 and it's demise in the Potomac. They found themselves without energy, far down the runway, and didn't increase thrust and didn't reject, but drove it off the end. Different reasons, but if we find ourself at a place where the airplane won't fly and we're fast running out of ideas, airspeed, and runway, then we have to do something. If the rotation attitude isn't producing adequate AoA to fly away from the runway, then increasing AoA with an attendant rise in drag may not be our best option, especially if we are going to go past the maximum rotation angle. Thrust may be our friend. Max braking, reverse to a stop, and EMAS, too.

You mention striking the "skid plate," which sounds a bit dismissive; a tail strike if very often more than dragging a plate; it's damage to a bulkhead and skin and rivets and can lead to other problems such as damage to control surfaces or internal controls (eg, stab trim jackscrew). It's more than simply taking advantage of a "skid plate." Rotating past the max rotation angle is taking a massive gamble that one ought not until every other option is exhausted. Moreover, if one doesn't have the energy to go fly, be it adequate lift, thrust, speed, or whatever combination exists that is insufficient, increasing drag and forcing the airplane into the air in a low energy state is also a very big gamble that opens the flight to a host of additional problems.

Pitch does equal AoA, but AoA does not necessarily equal lift. Moreover, in addition to an increase in induced drag as a function of AoA, which is a substantial rise with smaller and smaller increments of AoA as AoA increases, dragging the tail down the runway increases drag at the expense of structure, and further retards the ability to accelerate.

You missed a few options, among them decreasing AoA, using the remaining runway to accelerate, while increasing thrust to max. Treat it like a windshear beyond V1, rotate in the last 2,000' if needed, but if one lacks the speed to come off the deck at a given energy state and weight, pointing that nose skyward and burning down the runway is not the best choice, any more than horsing the airplane off the ground regardless of whether it's ready to go fly.