The company therefore removed the VMCg tables from the QRH as we do not need it anymore.
Don't like that. So your company doesn't have any interest in the interplay of Vmcg and crosswind ?
I don't like it either to be honest. However as we have to stick to the performance program figures anyway there is not much we could do in any case. On the classic VMCg was pretty high compared to the NG though, so the issue is basicly non existant anymore. Even on the short one (700) we achieve VMCg values well below 100kts (yes, i have the old tables stashed away for my own usage, and there is allways the AFM).
VMCg is only fixed for a thrust setting, since thrust settings are not fixed though it is another value that can be played with.
Now that's just plain dangerous thinking. Vmcg is fixed for the rated thrust setting. When you flex (I'm presuming that you are so referring) the Vmcg stays the same. When you derate, the rated thrust and Vmcg reduce. Beyond that you have no option to play with the numbers.
Quite right, but it is not a fixed value for all operation anymore as we do have the freedom to use different thrust settings and use that freedom nearly every take off. In fact i used full rated thrust only once or twice since changing onto the NG, every other take off was derated in some way or another (and "flexed" too of course).
All in all take-off performance is not one-dimensional, we have so many different things we can change that there are allways several solutions for a given problem. We have 5 different take off flap settings, we have 3 different thrust rating, we can use ATM additionally, we can change seamlessly into improved climb speeds increasing our Vr/V2 by up to 35kts, or choose not to do so, use tailwind up to 15kts. Boeing made the 737 a pretty versatile beast.
For the given problem, VMCg too high, the software would most probably simply reduce the thrust setting by a notch and with that the VMCg, given that there are no other restrictions.