Well first of all, religion is meant to be absolute. Which implies that there's no need to learn anything away from it because it is considered the 'best.' The syllogism would be correct if that premise were to be true.
Also, people might be 'powerless' (I'll get to this word in a little bit) because they have 'full' confidence in God's Will. They rely on Him for their power. And the mentality behind this would be that since they are preaching His Will, karma will surely happen and they'll be offered good consequences for their insightful support which is in some way powerful.
To define, "powerless" you have to first understand the philosophy of it; what factors are taken into account to claim something or someone is powerless?
And being poor also seems a little subjective. If by poor, you mean financially, then yes, there might be a tendency for religious people to be poor, but if you're self-aware and self-actualized, you're one of the richest people in the world; in history. That's their main goal, that's everyone's main goal, but everyone has different approaches to achieving that goal.
If they're financially poor, it's because they focus mainly on not concerning themselves with greed, or jealousy. Historically, if you look back, most religious icons were financially not well off. They believe it is sin so they try half-heartedly to make some kind of living, no matter what it is, as long as it doesn't stray away too far from what they are 'allowed' to do.