How important is it to be at least good at everything? It is essential to have a person with superficial knowledge of everything. How else will that person identify a problem before solving it? Knowing that there is a problem in a domain is half the work done towards solving it. A specialist can’t identify problems not pertaining to his own field. A generic problem-identifier is cheaper than a specialist problem-identifier for each domain.
Don’t general problems vastly outnumber specific problems? It takes one person to drive away birds, keep an eye out for parasites and graze cattle away from the field. It will take one person each to study the pH balance of soil, predict humidity and intensity of sunlight; things that hardly pose a problem to the average farmer.
How useless is a specialist outside his domain? He will just be a passenger, a spectator. You don’t require to be a brain surgeon to bandage an abrasion. The local car mechanic isn’t really a rocket scientist. An electronics engineer can’t (still) fix a malfunctioning fan.