Well, I can give you Russian oligarchs - they came to their wealth during time of chaos, and mostly through stealing. But Texan oil billionaires? They won their wealth fair and square, if not for anything else then for just recognizing an opportunity and acting on it. Believe me, there are many people in this world who would blew it in stupid ways.
I won't even argue about Texans even though you're wrong there, but since you accepted Russian oligarchs as a problem with this world view that having money = having contributed to society then I'm not sure what else to say. You already admit this model doesn't work as a proxy to merit in the case of using force and connections.
Take another example, someone who won a lottery vs someone who hasn't, but otherwise lived the same life, in your world view one deserves it and the other doesn't. And their their offspring forever on as well? If you accept this now your list of exceptions is using force, connections and also luck. But we can keep adding examples and exceptions to the rule until at some point you need to admit that way of looking at the world is too flawed, no? BTW this luck aspect is the same as the "Texan got a knock on the door offering them millions forever because they have oil under their house" so I guess I did end up re-arguing that.