I think you make an excellent point about Eli. However, even godly parents can have bad kids. Samuel's children did not "walk" in his ways (1 Sam 8:5).
The scriptures are interesting in that there are numerous stories about godly women helping their children but it's next to impossible to find an example of a godly father/son relationship. I'm reminded of this every father's day. ;O)
BTW-For clarification, I'm reminded every Father's Day at church when the pastor has a very hard time finding a Biblical example of a great father/son relationship. I am fortunate to have a wonderful son who I enjoy a wonderful relationship with. It is only because of God's grace.
Yes, you are right. I forgot about Samuel. And it is true that even godly parents can have children with more of a propensity for doing rotten things than others. My guess is, that since some have been ultra-blessed in this department, they WILL, without a doubt, be tested more than others. That's where one cannot just sit back on their laurels and think God will rescue them and their children, without so much as lifting a finger. Everyone will be tested to the point which it can be dealt with. More blessings=More testing because there's more resources to solve problems. But, in the end, we're all just people who have problems to solve, and each person must be responsible for solving their own problems. Not government or some other such thing, as many are led to believe.
BTW, I also think Jeremiah(the weeping prophet) is a good example of a father/son relationship. He remained loyal to God, the father, to the point of just being a, bearer of bad news, simply because the people would not listen at all...