Fitness is activity specific. For example; a weight lifter can be very fit to lift large amounts of weight whereas a person who is fit for long distance cycling may not be able to lift much more than the bare bar. Another example: A sprinter can be very fit for that but inadequate for a marathon.

Plus, mental fitness, or toughness, is a key element that is often ignored by the kind of metrics proposed above.

Nope, fitness is not a one size fits all thing.