Your watch looks like it has a very good example of an engraved dial; these are popular among collectors. The crystal does look like a plastic one that has aged. It shouldn't be hard to find a replacement either in plastic or in glass.
I like the Illinois 12-size watches; they're very nice to carry. Illinois must have found them popular, too, because they made almost 400,000 of this particular movement between 1911 and 1929, under their own name and many private labels.
I'd certainly think it worth getting serviced and getting a new crystal. A well-made movement like this probably has another century of use in it with a bit of care.
And then, if it's a family watch, it is a good candidate for being kept as an heirloom.
Thank you very much for the info. I will have to see if I can locate a glass crystal as I think it would be more appropriate (?)
The dial is interesting, unfortunately it is dirty, so a good cleaning most definitely. The size is great, not bulky at all. I have no idea how this watch came to my grandfather, it was one of dozens he acquired over the years. And it will be kept in the family, as I have a German 8 day walnut wall clock that was his as well.