A "general intelligence" may be capable of learning a lot of different things, but possessing capability does not equal actually having it. The "AGI" must learn...and that learning process can take time. If you want an AGI to drive a car or play Go, you have to find some way of "teaching" it. Keep in mind that we have never built AGIs, so we don't know how long the training process can be, but it would be safe to assume pessimistic estimates.
Contrast that to a "narrow intelligence". The narrow AI already knows how to drive a car or play Go. It has been programmed to be very excellent at one specific task. You don't need to worry about training the machine, because it has already been pre-trained.
A "general intelligence" seems to be more flexible than a "narrow intelligence". You could buy an AGI and have it drive a car and play Go. And if you are willing to do more training, you can even teach it a new trick: how to bake a cake. I don't have to worry about unexpected tasks coming up, since the AGI will eventually figure out how to do it, given enough training time. I would have to wait a long time though.
A "narrow intelligence" appears to be more efficient at its assigned task, due to it being programmed specifically for that task. It knows exactly what to do, and doesn't have to waste time "learning" (unlike our AGI buddy here). Instead of buying one AGI to handle a bunch of different tasks poorly, I would rather buy a bunch of specialized narrow AIs. Narrow AI #1 drives cars, Narrow AI #2 plays Go, Narrow AI #3 bake cakes, etc. That being said, this is a very brittle approach, since if some unexpected task comes up, none of my narrow AIs would be able to handle it. I'm willing to accept that risk though.
Is my "thinking" correct? Is there a trade-off between flexibility (AGI) and efficiency (narrow AI), like what I have just described above? Or is it theoretically possible for an AGI to be both flexible and efficient?