It's interesting just how different experiences can be at different tables. For me, knowledge checks most often come up when a player needs more information to determine whether a potential course of action is feasible/wise. Examples:
- Upon seeing a mercenary company insignia, and considering a plan involving distracting the mercenaries. "Does my character know whether that company has any strong rivalries with other companies, and what their rival's insignias are?"
- Upon considering a profoundly direct method of bypassing an enemy fighting at an interior choke point. "Is my character familiar enough with the architectural style of the building to know whether this wall is structural?"
- Upon noticing a storm system moving in and considering waiting for it to pass. "Is my character familiar enough with the weather patterns in this region to be able to make an educated guess as to how long the storm will last?"
So not only are the players at my table not trying to get access to rulebook information, they're usually asking for answers to setting questions I've not previously considered and don't (yet) have answers to.
That's a cool system. Ironically enough, however, I would personally find it extremely immersion-wrecking. For me immersion requires the game world to feel like a real place, and being able to readily see that the new complication that just arose was added as the result of a bad die roll on the tension dice would work against. Oddly enough, I'd have no problem with the DM just deciding to add a new complication because they think it would be fun, as long as it was presented seemlessly with the rest of the world--it's seeing the tension mechanic in action (or knowing it was in use) that would cause the problem for me.
I feel the same way about wandering monsters. I'm totally fine with using dice to abstractly determine whether an
existing monster in the area happens to wander by as it goes about its business. And I'm also totally fine with the DM choosing to add a
new monster without rolling any dice at all (again assuming the revision was seemless). But fighting a monster that I know wouldn't even exist in the game world but for a bad roll on a wandering monster check makes the game world seem less real to me.