Why do some Eagle devices have minuscule value labels?
Why were these packages designed this way?


I can't say for sure why you have the very tiny label on that particular part. Perhaps the idea was to make it "disappear" without deleting it altogether. This allows it to still appear on a BOM, for example.

In general, the value field is not normally used in the silkscreen at all, except maybe in certain educational projects or kits.

Normally, the value field is used only in an assembly drawing, where it just needs to be small enough to match the general size of the part on the drawing.


  What is the best way to fix the errors caused by these labels?


As I said above, simply don't include the value field in your silkscreen layer. This is why "names" and "values" have their own layers in the design stack.

Otherwise, it would probably be worth your while to create a custom library that has the labels the way you want them.