There are certain things I love seeing in a storyline that resonate with me. Redemption is pretty high up on my list of themes I enjoy exploring. I remember seeing Star Wars and being blown away by the idea that it's never too late. When written right it gives the characters such depth and pathos. It's a huge reason for me preferring Angel the series over Buffy the Vampire Slayer. I think it plays a part of my interest in certain characters.
A big part of Boosters' is his screw up that cost him everything in the future. In an act of desperation he risked everything to start his life anew while making his situation worse in his own time (stealing the time sphere.) But he became a hero. True he sells products but he actually cares and wants to do the right thing. Because the guilt of his scandal will always weigh heavy on him. Sure there was a retcon to make it partly about saving his mother but there was still selfish reasons involved. Booster was a poor kid that wanted it all. Even the add on about his dad was about him putting something he wanted (his dads' love/approval) over what was right. These flaws deepen his character and set him apart from other heroes.
I think part of the reason Batman supports him is because he sees that Booster is honesty trying to rise above his past.
That surprised me because DC hasn't been that great with shades of grey in the past but I think their trying to do better now. I'm just glad that Booster never got dragged through the mud like others.
My favorite bat characters? Jason Todd, Cassandra Cain and Stephanie Brown. All of the have gone through various degrees of redemption, Jason is currently going through his own after writers went too far in previous canon.
It's not the sole or main reason for me enjoying JLI and RHATO but it plays a part. I like character development, sometimes that goes the other way (Cry for Justice) but seeing the characters get up and strive to be better? Yeah, that keeps me picking up month after month.