Exercise Variation

How are you doing, coach?

When strength training is focussed around strength skill, as far as I understand, the most important aspect is the skill in THAT given lift. That in contrast to systems based on less frequency/more volume or Westside, which focus on different mechanisms of strength building.
When strength has to be used for different things than the given lifts: as an example, an unforseen event at a Crossfit game or Strongman, or when training for Football, how would you prefer to train?
Wouldn’t focussing on a specific lift have drawbacks, like being great at the specific lifts, but lacking bleed over in different movement patterns?

Seeing forward to your answer!