That’s the reason. Below 80 knots you push the yokw forward to get weight on the nose wheel for steering and after about 80 knots steering is done only using the rudder.

I guess elevator down in the first part of takeoff roll, is done in order to transfer the most weight to nose gear and hence to give the most possible directional control in the low-speed part of the takeoff roll, when the rudder has no or little authority.

Real aircraft (not all) Boeings for example don’t have this in SOP, put full elevator down below something like 80 knots at which point they centre the controls and wait for the plane to reach the v speeds and then take off. If I had to come up with a reason for doing so, I’d argue that the weight transfer of the aircraft at throttle up puts the plane closeish to the tipping point and deflecting the elevators in such a way deflect what little airflow is occurring over the elevators from the engines to create as much lift at the rear as possible but this is just a guess based on logic.

As for the X-Plane video, it does look like the planes take off at stall speed to me which might explain why they level off to gain airspeed soon after (I would guess there’s some low airspeed protection logic built in). I think the best thing to take away from the video would be to just accept that it’s in development and it’s obviously not perfect yet.