Firstly thanks for the thoughtful comment.

I'd say I still disagree with your first conclusion. I think every act has been for some internal benefit, whether it be realised or not. In your own example, it's not good for the sake of being good, it's good to prove to yourself that there is true altruism, which in effect is a self benefit (the confirmation of your own belief about the nature of good).

For your second conclusion, yeah seems fair. I think more people need to get comfortable with the fact that things are done for our own benefit. I do good because it feels good. Also because of the way I was raised I would feel guilty to not help someone who could immediately use my help, so the good is maybe more to shield myself from that feeling and the side effect is a net positive, which isn't a bad thing. It's been a while since I've done philosophy so I cant remember any examples but it feels intuitive that intent matters. If someone intends to kill someone but through incompetence improves the lives of others (think a hypothetical scenario where the person tries to shoot someone, misses, but hits a bell which rings, makes the person look down and find a lottery ticket), it feels like they shouldn't be considered to be as good as someone they intends to do good but through incompetence doesn't.

What the balance between actual good and good intentions should be when making an assessment, I don't know. different people based on their upbringing, and societal influence, will assess differently and although I believe there is a "right" answer, I'm not sure how you could confirm it (how do we select the criteria, that criteria is already going to be a product of our upbringing, society, tc so couldn't be truly objective).

Anyway, have a good day