Remember that voltage regulators can have quite large voltage errors.

And since you subtract a quite large offset, small voltage differences in the voltage reference - how much you subtract - will make a big difference in your scaled signal you feed to the ADC.

Your input signal have an offset of 8.5V and a total swing of 0.5V.

So every 0.01V your offset voltage varies, would represent 2% of your measurement range. In short - you can't afford much drift in your offset voltage.