The amount of precision required for reading glasses is a lot lower than that required for distance glasses. The reasoning is that you can easily move the object near your face to get better focus, but you can’t really move the world to get better focus.
This is especially true as the focus precision is exponential to distance: around 30 ft/10 m away is basically infinity*, but there is a huge focus difference between 1ft and 1.1ft. This means moving a a few meters closer to an object 40 ft/13 m away will make almost no difference, but moving a book a couple inches/cm will make a huge difference.
That said, optometrists can do a much better job making reading glasses, its just often not worth the extra cost.
* Higher precision is required for some stuff, namely if you have really high magnification. Think telescopes and binoculars.
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