What's the point of an original air temp sensor if the ECU over rides it's information?
That is a good question actually. @Roger 04 RT has explained how it all holds together.
But why?
Here's a bit nerdy stuff. If you don't have time to read it all, go to the last line

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It's a bit complex, but I'll try to narrow it down.
If the fueling relied it's fueling entirely on O2 feedback, keep in mind that at any condition, the fueling first decides the amount of fuel to be delivered, then the fuel is delivered to the cylinder, the fuel ignites, and THEN the verdict of the prediction is given from the O2 sensor. I'e the sensor at best will tell you how it WAS, not how it WILL BE.
In steady riding conditions this one-step-behind approach will work, sort of. But in order to make the engine run half way decent, there would be need for some extra fuel, and with current emission regulations the engine would not meet the standards.
And there is one more issue. The engines with a CAT uses the CAT to convert the CO from the exhaust into CO2. For this to work, the Cat needs oxygen from somewhere to tie the extra Oxygen molecule to each of the CO molecules in order to make it a CO2.
It's mentioned that the ideal combustion is AFR 14,7, and this is where ALL the fuel is burned using ALL the oxygen from the air. But if the engine ran at a steady 14,7, there would be no oxygen left over for the cat to convert the CO into CO2.
In order to provide excessive oxygen into the CAT, the fueling needs to slightly vary the mixture rich/lean in order to make the AFR oscillate between AFR 14.0 and 15.0 (or there about). If the fueling was to rely on the feedback alone, it would be like and endless chase, a bit like a dog chasing it's tail. Instead the ECU takes the readings and calculates an average that it uses to compensate on the fly. Since the fueling is more or less accurate already, the adjustments called for by the feedback from the O2 are relative modest, hence they call it trim. And since it's continuously adjusted, it's called the Short Term trim (STT).
Since there is a desire for the best possible fueling at any condition, preferably without the need for adjustment based on the feedback from O2 (remember, O2 is always one step behind), the value for the STT is also stored for later use, in case it's a lasting condition (like an air leak or clogged airfilter). The STT is therefor compared to the value of the long term trim (LTT) in the LTT table, and the LTT trim table is adjusted accordingly, by small steps each time. The ultimate goal for the ECU is to obtain 0 correction from the STT. The LTT trim value is ALWAYS part of the calculation of fuel.
But even LTT values are corrected in small steps each time, over time it has the capability to make fairly rich/lean mixture. Hence, the BP may work to begin with in some engines.
When I developed my own O2 manipulator, my first prototype was built with the ability to falsify the readings manually, and I could easily make the engine run riche enough to where the exhaust went smoking black.
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Soo... Why do they do it the way they do?
It's done in order to make an engine drivable and at the same time meet emission standards.