I have worked on so many vintage instruments over the years where the finish on the back of the necks have been completely worn off. They are fine and just as stable as a neck with finish on them. The oils in your skin oil the neck naturally.....but you are always welcome to occasionally add a coat of oil if it makes you feel better.
^^^I wish this could be stickied.
The biggest issue in staining of the maple where the finish has worn off.
As a young bassist I was weirded out by grungy maple. Rosewood was supposed to darken, but maple... ewww!

Then in the early 80's I bought a really beat up 1964 P-bass from a local shop. I've posted pics before, but here's the neck:
Not a great pic, it's even darker in person. The look wasn't my thing when I bought it, but it was the only vintage Fender I could afford: $450, Fender case included! Beat to hell and back, but it was lightweight and the tone was to die for. I also realized the neck
felt wonderful. For me it was way better than the standard gloss poly, but also better than other finishes. Largely because of that, I decided that the grungy look didn't matter to me at all.
Wasn't just that bass. I used to regularly visit shops that had old Fenders (a lot more common back then). I even got to play 50's Fenders, including a '51. I realized I liked the worn-away necks better than the intact ones.
Obviously, this is all just a matter of taste/opinion. I'm not saying that I've become "enlightened", but only that my opinion of the look was changed by my opinion of the feel. That is all.