But that's the thing, I don't think (at least from how I interpret his behavior) he is insecure or doesn't believe in himself. He knows he's strong and he isn't afraid to display his power when the situation warrants it. Remember when the house was burning down and he put the entire thing out instantly with a spirit summon that dwarfed everyone else's that we had seen previously (almost like the chapter was specifically setting up the reveal that he's crazy strong). He knows he's strong and I'm fairly sure he's made some side comments about how his power makes him weary implying something happened in his past that made him want to relax and take things easy.
Point being though, he's so sure of what he wants out of life that he doesn't mind all the people constantly berating him or putting him down because he lacks ambition. He purposefully doesn't seek grander heights because he's content with where he is already. A lot of you are confusing someone who is passive as someone who is a doormat. Do you make it your life's mission to prove a child wrong when they call you a loser? No, you just ignore them and smile it off like water off a duck's back. Their opinions are inconsequential to you (or should be) so why would you pay them any heed?
And again the important bit that Washio himself has stated, he could climb the ranks if he wanted to but that's just adding more responsibility and work for him to do which would take away from his current laidback life. What would he stand to gain other than people's respect, people who he doesn't really give a shit about? If the story does go in the direction of having him get promoted and "prove himself" I guarantee it will only be because his monster girl students convince him to because they feel it reflect poorly on them to have their BAE getting ridiculed. Alternatively but in the same vein, something happens that prevents him from helping his former students due to some bureaucratic bullshit and his low ranking excludes him from having a say so he climbs the hierarchy to ensure they are treated well. Either way, it will NOT be because he suddenly sees his current life as problematic and suddenly become ambitious. It will be in an effort to help people he cares about since otherwise he couldn't be bothered.