If the glimpses into his childhood and young adult life are anything to go by, I don't think Saitama ever had anyone who'd stick by him, and especially not when he needed them most. When he got picked on by bullies at school, when he was struggling in class, when he was suicidal after his job interviews went poorly, when he was living in apartments that were dirt cheap because they were crime fronts, when he was barely eating 'cause he couldn't afford it, when he was working himself into heart attacks, when he started to go through a massive, startling, scary transformation that was alienating him even further.... Saitama doesn't seem like he has EVER had a single person to rely on when things got bad.

All those times he was little and fantasizing about heroes or on the brink of death and wishing he had a guarantee that he'd come out alive so he could push himself further, I think that's the kind of hero he was imagining--someone who, when everyone else falls, will be there to make sure they're safe no matter what. He seems like he wants to be a safety net so nobody ever has to go through what he went through, and what hurt/scarred him so fucking bad. That's why he doesn't spring to action immediately--he lets people give it their best shot first, but WILL drop everything to finish things up for them if they can't. That's also why I think he brings up always being a little too late when Genos tells him he's right on time early on in the series. He notices he's late because he WANTS to be right on time. He wants to be that ideal hero who magically swoops in at exactly the right moment to resolve things instantly and leave everyone to live their lives again.