When I select a single imported segmented curve, the simplify path option behaves as expected. Although I need to select it multiple times in order to get the best result.

However, when I select all imported lines in the entire document, the simplify path option (even on the very same line) behaves very differently and completely destroys the look of the objects!

Why is this? There seems to be no visible options for the tool at all?

You have encountered a quirk of the simplify function. The amount of simplification seems to be proportionate to the size of the selected shape. This means that large shapes lose more detail than small shapes. Sometimes I try to remove excess nodes from an imported pdf and the outcome is unrecognisable.

I have two suggestions. Open Inkscape's preferences [shift+ctrl+p] and navigate to [Behaviour] and reduce the value of [Simplification threshold: x.xxxx] for less aggressive action.  Alternatively use [Path > Path Effects...] [Simplify] and adjust the parameters to vary the amount of simplification applied. When you're happy with the result you can permanently apply the effect with [Path > Object to Path] or choose [Flatten] in the dropdown box in the path effects dialog.

http://tavmjong.free.fr/INKSCAPE/MANUAL/html/Paths-Editing.html#Paths-Misc

Thank you for the information!

Unfortunately, the "path effects" only works on a single path, and I have about 10,000...

Also, I'm a bit word blind, but that documentation quote doesn't seem to mention the quirk, and neither does that preference, which seem to imply that it's an absolute relation to the document DPI (which it really should be).