This information ... has nothing to do with an engine failure scenario which does not consider crosswinds or contamination in terms of directional control.
Are you sure of that ? Perhaps you can cite appropriate references to support the contention ?
it is always safest to continue and always less safe to reject after V1.
Almost always the case and, by far, the preferred habituation for crews on a simple risk management basis.
However, not if, for whatever reason, control is lost or there is some other circumstance which precludes a sensibly safe continued takeoff.
The commander should consider such events as part of his general development and preflight considerations
How many airliners will takeoff with a strong crosswind today.
Many will of course.
However, the Vmcg concern with crosswind generally is not a problem in routine line operations. It presents in very limited circumstances and only for a quite small range of speed in excess of Vmcg - the centreline deviation characteristic curve rapidly moves out of the problem area .. which is why we don't fuss too much about the topic in routine operations ..