And, if we sit back in the smoking chair and contemplate the matter over a wine .. why are we launching at minimum speeds ? If the runway is longer than needed and it is just a case of low weight .. why not adopt an appropriate higher speed schedule and avoid most of the worry ?
"Launching" at minimum speeds? For once, John, I find your logic rather difficult to follow.
All take-offs start at a speed at or close to zero. We'd like most of them to end at a sensible flying speed as we climb away. Unless you have invented an alternative to Newtonian mechanics, that means that at some stage we have to go through all the speeds in between.
I think I understand what the certification "promises" are if an engine fails above Vmca in the air. I also understand from FAR 25.149(e) what the certification "promises" are if an engine fails above Vmcg on the ground. And yes, such certification "promises" are based on ideal conditions that are not necessarily replicated in the real world and are probabilistic, not certain -- that doesn't make them entirely worthless from a risk management point of view, just subject to the usual disclaimers.
But I don't know what, if any, controllability requirements follow an engine failure below Vmcg on the ground. There might, for example, be a requirement that control can be maintained if the power on the operating engine is reduced within a specified timescale, or that nosewheel steering must be sufficient to maintain the centreline. Or there might be no such requirement at all -- that seems to be the implication of your post.
Understanding what is "promised" under what circumstances by FAR subparts 23 and 25 provides a useful background for understanding the logic behind operational procedures.