Why are Illustrator measurements often not precise?

One thing that constantly frustrates me is that Illustrator invariably doesn’t allow me to create precise measurements.
For example, if I create a new document with an A4 page then draw an A4 box, the new box is not 210 x 297 as it should be but 210.002 x 297mm.
It doesn’t matter if I correct the inaccuracy in the Transform box. However many times I correct it and save it, as soon as I check the box size again it still says 210.002 mm.
Is there a fix for this?
NB. I have my units set to millimetres. I’ve have deselected ‘Align new objects to pixel grid’ in Transform

Thanks for replying Jacob.
At least I now know there isn’t a solution.
I’ve just discovered that if you create a new Print document with a default A4 page, the Document Info box says it's actually 210.0016 mm x 297.0001 mm. I guess that ties in with what you are saying about points.
I’m amazed that Adobe haven’t found a solution for this over the years. I wonder how many thousands of man-hours have been wasted by Illustrator users all over the world trying to fix the unfixable?

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