A somewhat less direct concern but a related one is ground effect lift. the aircraft can remain a short distance off the ground (roughly a wingspan of altitude) at lower speeds than it can actually "fly," due to ground effect. Smaller aircraft might routinely spend some time in ground effect gaining additional speed before they begin climbing, but airliners have so much thrust they usually rotate pretty directly to their climb speed. This makes it more of an issue though that if rotation occurs too far before Vy climb speed the ground effect period will be prolonged and increase the amount of time the aircraft spends at risk, flying but slow with poor control authority and too close to the ground to have much of a recovery opportunity. The ground is a pretty safe place to be, the sky is a pretty safe place to be, but that first couple thousand feet between the ground and the sky is rather hazardous and jetliners get out of it as quickly as possible.
Then the problem here is trading safety for something - cost apparently.
BTW, in a small plane I found soft field takeoffs quite fun. Nose up early, wheels up early, fly in ground effect to gain speed. I suppose that is a safety tradeoff and might not want to do it in some conditions.
Edit: Actually, that probably doesn't even come into it. Not a pilot, but don't imagine "barely rotate so the nosewheel is in the air but still have negative angle of attack so no lift" is very easy, or very stable if possible. Even if you could do it, you'd risk slamming the nosewheel back into the runway.
So, once you get to the stage where you're ready to rotate, or even late in rotating, you're committed to getting the plane off the ground.