I do not think that anyone here completely understands what "idle relearn" is. However, it is documented in Honda literature found on this site.
I believe that it is a procedure to follow after making changes to engine components that impact fuel delivery amount calculations, that pulling the battery erases the memory that holds the adjustments to fuel delivery at different RPMs and engine loads. Please don't rely on my interpretation, which is that these parameters need to be restored, and I believe that for this to happen, the engine must be operating at temperature at every specific RPM and load (as determined by manifold air pressure) for which a value is recorded. Obviously this might take a lot of driving in various conditions before the map is completely reconstructed. And that as components change, the map values need to change, and I believe that long term fuel trim may be a window into this. (Documentation for this sucks; we need a dump of the firmware.)
I believe that "idle relearn" simply ensures that the portion of this map around idle speeds is rebuilt properly. I believe that it won't happen until the engine reaches operating temperature. There is a question in my mind as to whether Honda's advice to hold the RPM high using the accelerator at the start is just a way to force the engine to reach temperature faster in the shop and save diagnostic time. I've read that others drive the car until it is hot, then pull the battery for the same effect. (Not often possible in a shop environment). And that others just let it idle until it reaches temperature. At some point the values are stored. Since there is no magic "Done!" bell, the time to wait after reaching temperature seems arbitrary.
Seems to me that performing this arbitrarily may work wonders for some and do nothing for most for a lot of reasons. But that for all, the rest of the map must be rebuilt, and this takes time simply because of the need for the vehicle to visit most or every point on the map. I give myself two tanks of fuel before relying on the MPG meter, for instance.
I have seen terrific mileage the first few miles after an ECU reset when my car was running off defaults only to see it drop as the car based the new map values on measurements from faulty parts performing out of specification. That mileage returned when I replaced those parts.
Again, until Honda releases ECU source code or an Insight engineer spells it out in gory detail, what I have written is heresay based on what I've been able to gather reading many articles on the web. Sadly, many of those are uninformed, speak of different technology, are clickbait regurgitating handwaved explanations, or are just wrong, and the credentials of the authors of the few documents that seem authoritative seem to be uncertain themselves. This is due to the actual details of our cars' operation being proprietary and therefore opaque. In other words, do not rely in what I have just written; I could be wrong about important points.
