In those situations we're talking about people who have very well established backgrounds that makes them prime choices to take those sorts of stations. Riker, for instance, has been established to be one of the best pilots on the Enterprise, a very good tactician and previously has held high ranking engineering positions. It makes sense for him to take tactical, the helm or ops in a crunch. Chaktoay? Not so much. He's always come across as a thinker and an explorer, not necessarily a "doer".
O'Brien, as you pointed out, has a whole slue of very well established backgrounds in both engineering, tactical and to a lesser extent, command (as far as that will take him being a non-com).
In a crunch, it seems like a better solution on Voyager for the relief officers to take over positions instead of someone like Chakotay; you know, those guys who have hundreds of hours of experience running that position? I mean seriously, who would you rather have take the helm? Someone who has been piloting Voyager ever since getting to the delta quandrant or someone with some semi-regular, mostly recent shuttle piloting experience and was never established as any kind of exceptional pilot?
I suppose its a little weird for us where Voyager is concerned. Its the first ship we saw where both the captain and the first officer came from the sciences division and not the command or engineering/tactical division.