Hi
Well they're not battle scars in truest sense, just a myriad of little scratches that come with wearing a watch - if you want it to be pristine, don't wear it , but that's no fun.
So would I get it polished - I think so, to bring it back to how it was. I've had other watches serviced & they were polished too - came back looking perfect for a bit. If I'm honest didn't think about saying don't polish it.
I do have a vintage piece 65+ that when it's serviced I will be more specific with, as I'd want it to look honest & its age. If it came back highly polished & looking perfect it would lose some of it charm - but it is personal choice on what you'd like.
So do what you want if you like it - it's your watch after all
Cheers
JML