This logic only holds if you take an extremely narrow view of what constitutes self-interest. If you broaden that understanding to include the benefits we receive from wider social progress, then doesn't this chain of reasoning fall apart?
Aligning one's interest with the broader public makes sense because we are part of the broader public. What benefits the broader public benefits us individually, too.
Yes, but the inverse is not true: what benefits oneself doesn't necessarily benefit the broader public. And that's what matters when looking at individual behaviors.