And you're exactly right of course. The narrowband sensor does one thing only, and does it very well- it tells the ECU that the a/f ratio is either rich of stoich or lean of stoich. But not how far.
The factory ECU fuel control algorithm is speciall designed around that sensor type. All it knows from feedback is the the mix is either rich of stoich, or it's lean of stoich. It doesn't know "how much" though. Then it just seeks to continuously vary the mix rich/lean/rich/lean. The faster it varies rich lean/rich/lean, the less far the rich and lean excursions are, and the average is then closer and closer to just flatline stoich a/f ratio, which is (usually) the goal when it's in closed loop and looking at sensor feedback. That narrowband closed loop fueling algorithm type is generally called a "ramp and jumpback" algorithm. It works great for cruising around.
The factory ECU scheme can't generally control a/f ratio to a target a/f ratio away from stoich. Because it get's no a/f ratio feedback for one thing, other than "rich or lean of stoich (but not how far). And what a coiky-dink, we are usually more interested in best power a/f ratio, which is well rich of stoich. That's why "it's good enough for the factory ECU" doesn't really apply here. We're trying to do different things than the factory ECU is.
When you have a wideband sensor, now you can just use a linear type control scheme, because now you also know "how far" you are from your target a/f ratio. The two schemes are different.
TurboTR