First off, their success is undeniable. A case could have been made that at the turn of the millennium that they were one of the most successful and popular bands in the World. They ushered in the second wave of Pop-Punk and packaged it in a way that showcased angst in a shiny and dare we say tongue in cheek way. They were all over the radio and they ushered in many imitators, thus meeting the influence category that the Rock and Roll Hall covets.
What works against them is that blink-182 was never regarded as a deep and introspective band, even in the songs that recorded that showed that side of them. A lot of their music was dismissed as juvenile and it was not like skate punk music was considered cerebral. They were a skate punk band though were never apologetic about it. They were what they were.
Regardless of what side of the blink-182 fence you are one, this was a band that dominated for a time and inspired many young kids to pick up a guitar and a skateboard.