O'Brien also has a history with the Cardassians, too.
True, and he is also the one who has to wrestle with this alien space station that keeps malfunctioning, so there are a few things that seem to anchor him in the ongoing story moreso than Dax and Bashir.
The DS9 cast of characters involves a lot of aliens and exiles, and I guess you could say that O'Brien is an exile in a sense, on this "Cardassian monstrosity" of a space station that he constantly is at odds with, a bit like Garak, for whom the temperature is too low and the lights too bright. Except for O'Brien it's that nothing ever works the way it should. This fits with the "torture O'Brien" theme.
Bashir and Dax seem a lot more detached and detachable from the main storylines, though to the DS9 writers' credit, they never give up on any of the characters and keep throwing story ideas at them until something sticks. Eventually with Bashir what works is his fascination with covert operations, first Garak's appeal to him, then the Bond holosuite game, and finally of course Section 31.