Do you think it is possible for LWers to perform this service for each other on this forum, or does it require much closer interactions and/or intimate knowledge?

This could have perverse consequences, because "You don't seem very curious about this" seems like a criticism.

In my case anyway, having an irrationality-cop would have two effects. First, it would motivate me to avoid the criticism by being more rational (like it does for Eliezer). Second, it would motivate me to avoid the criticism by hiding my irrationality better. The latter effect would be bad, because then both the cop and I would overestimate my level of rationality. (Why would I, too, overestimate it? Because I'd hide my failures from myself as well, in an unconscious effort to hide them from others more effectively.)

I think the fundamental issue here is that I dread criticism. (Solutions to this problem include exposure therapy and CBT.) People for whom this is less of a hurdle are likely to benefit more from having an irrationality-cop.