Haven't read this article yet but remember an Is This It oral history Pitchfork did a few years ago. Will give it a read later.
I was a huge fan of them at the time and I can remember being frustrated by how long it took them to follow up Is This It. That now seems silly as it was only just over two years, which is no massive gap, but it felt like an eternity to a lazy workshy teenager like me. In between the initial wave of interest that surrounded the release of the debut and 'Last Nite' all we got for over two years was the Someday single released in the autumn of 2002. When they did eventually return, it was with a really good but fairly understated single (12:51). I got the feeling they always had a love hate relationship with the attention they received, seeing the benefits in terms of the success of the band but never being comfortable with it themselves.
I'd say Room on Fire was a very good follow up, kept the ball rolling. The wheels started to come off with First Impressions, which I thought was a decent record but received mixed reviews. I remember a friend at the time saying he had always thought of The Strokes as existing on a higher level than the rest, but FIoE finally made them seem human.
Their huge and lasting achievement was producing a brilliant debut that was both critically acclaimed and hugely popular, an indie band's debut going to #2 in the UK chart is impressive, especially at a time when shite like Crazy Town seemed to be in vogue. They definitely opened the door for a wave of acts over the next few years, some good and some bad and most of whom enjoyed more singles chart success than The Strokes. Aside from Last Nite they didn't really have a single that your ever day chump on the street would recognise.