This is one I disagree with Claviger on. Referring again to the Triumph "adaptive fuel systems' pdf you can find on the tune ecu site, it says that the fueling will not be adjusted by the trims produced from the 02 sensor readings in areas of the map that are richer than 14.5:1. This is because the narrow band 02 can only sense whether the engine is above or below 14.5:1, but not how much. The computer then nudges the fuel up or down until it hits that magic number. If you look at the AFR map, only the low load/low throttle area is 14.5:1. Running the 02 sensor will allow the computer to adjust the fueling during cruising to maximize efficiency, but as soon as you roll the throttle open it ignores the 02 sensor and provides fuel based on the F table corrected for air density. Running the 02 allows it to compensate for a particularly humid day, or poor quality fuel for example. Be careful as running the 02 sensor disabled for long will kill it. It has to be heated to prevent water from condensating on it, or it will die. That is the reason for running a plug if you don't want to use it.
If you get the tune totally dialed in, removing the 02 sensor doesn't matter too much (basically like running a carburetor, the system always runs open loop), but for a canned tune I would leave it in. It will make sure that the AFR is at least right in the cruising and idling area where you spend most of your time, which is probably why you notice it running better. My '07 is running a canned tune with the 02 on, and has been for 5 years. It definitely is over rich when under heavy throttle, but it still idles nice and gets good mileage when cruising.
For what it's worth, I'm tuning my '18 with a wideband o2. Once I get the tune dialed in, I will go back to the factory narrow band 02 for the reasons I mentioned above. Also, I'm the first to admit
@Claviger has way more experience than me, this is just the way I read the info I can find. I really hope he comes back and jumps in here. Maybe if we all tag him enough it'll light up his inbox and get his attention lol.
Regarding the use of O2 or not, I have revised my opinion over time, and no longer always advocate for it to be off, as you mention, a close canned tune with 02 on, is a good solution for a ridable bike that runs smoothly if you've no access to a Dyno.
I have not extensively tested O2 on/off and it's effect on fueling outside the O2 adaptation zones, mainly because I don't like running the bike lean, which it does with O2 on.
My original ascertation that it may/will screw up a dialed in Dyno tune over time was based on the ASSumption that the Kehin does "Long Term Trims", something almost every ECU does in 2018 (but may not have been included in 2003/4 when the ECU was being originally developed). Evidence does show it does long term trims.
A good test of long term trims ability is to go get a Dyno tune, then reset adaptation and see how it rides (it'll be lean everywhere). I did this, and it was horrid, there are a few reports on the forum of others with the same experience. To correct it, reenable the narrow O2, ride a day or two and it'll be correct all over again. Not deinitive, but a strong indicator of LFTs existing.
I do, however, stand by my advisory that best performance is achieved with it OFF using a dialed in Dyno tune for your bike.
The rocket will feel healthy anywhere from 12.5-15 AFRs, it's a very forgiving engine, so without wideband data it is very hard to say that turning it on hasn't adjsuted the whole map.
Mean best torque vs Lean best torque. MBT is higher than LBT, but, LBT will still feel good, and LBT is what you get with it on, so if you want all 150+lb-ft below 2,000 RPM, get it Dyno tuned and turn the O2 off to preclude the ECU from fighting the tuning work that was done.
Keep in mind, to get MBT you need to adjsut timing as well, so simply PC-V tuning for best power will show improvments, but will leave either power or mileage (or both) on the table to some degree.
MBT is achieved richer than 13.5:1 and leaner than 12.2:1 on most NA engines and the R3 is no exception.
Also, remember I'm full of ****, so this is all clearly information I quickly googled.