The two are inextricably linked. Accelerate, and the yaw departure risk disappears.
I fear that you have the cart before the horse. If a yaw departure has occurred then there is no option for acceleration to get out of the situation for Vmcg and only descent for Vmca ... the very thrust upon which you place your salvation's reliance is the same thrust which is taking you to your accident .... the thrust must be reduced to regain control. Like it or not ... we can't overcome the realities of the physics involved.
Be very aware that this sort of departure is quite rapid and ramps up very quickly over the spread of a few knots. Difficult to appreciate unless you either have been there or watched the aircraft gyrations under someone else's ministrations.
All multi-engine aircraft are Vmcg/Vmca limited.
Again, I fear you miss the point. A multi can be so limited IF the thrust/speed mix is appropriate. At higher speeds for a given thrust, the takeoff will be limited by some other criterion.
There are very few (if any) situations where an aircraft being used for training, with no payload and low-ish fuel (ie very light) NEEDS to be flown at, or anywhere near, limiting speeds.
I would agree. However, if you choose to use the standard min speed schedule .. and if that schedule is Vmcg or Vmca limited (which it often is) then you need to be aware of the potential for excitement in the event of a failure.
they all allow you to maintain an achieved speed ..
I'm afraid you have quite lost me here .. perhaps you might elaborate on your point ?
there is no need to ever go to the place you are describing. It's a theoretical exercise that only needs to be carried out in the sim.
This is not at all a theoretical exercise. Many aircraft schedule takeoff speeds at low weight which put you right in this sort of harm's way if you mishandle the failure during a continued takeoff. I think that it will be useful for the newchums if we continue with this discussion ?
So what is your point, other than semantics?
Philosophy and SOP. From a risk-based approach to things, the OEMs have, for quite some time, recommended such a black and white approach for normal failure situations.
For what it is worth, I always expect to stop until I hear V1, at which point I am absolutely going unless I cannot control the aircraft, or we have an uncontained fire.
The point is that, under the present paradigm, reaching V1 confirms that you are going to continue keeping on going ... ie if you aren't already stopping then it's up, up and away. (Caveat that this is predicated on "normal" failure situations).