… Doesn't Saitama does that already?

He usually saves people by killing the big bad of the week.
And he has inspired Genus, Blizzard and King to be a more hero like.

Heck, let's not forget one of his bests quotes.

Saitama will save people who are in danger if they're nearby, but he does it more out of basic decency than because he actually cares about saving people. King himself recently had to lecture Saitama about how being a true hero is about more than just fighting powerful enemies. Saitama has never shown any desire to connect with or inspire the people he protects, and even if he is by far the strongest hero, that doesn't automatically make him the BEST hero. That's the difference between Saitama and All-Might.