Wow, that may be the worst I've seen! There may be hope though.
First off, note that if you manage to file or sand those rough spots out, particularly that large gouge in the center bottom, you will undoubtedly widen the slot. The reason the slot is as small as it is, is because if it were too large, fabric would "collapse" into the slot. So with gouges that extreme, I would not try to fix through sanding or filing, as that's a lot of work for perhaps no good result.
My suggestion would be to try something far simpler: Use tape. What you want is something to render those rough surfaces smooth so the thread doesn't snag and tear. Try cutting a strip of packing tape--or who knows, maybe even Scotch tape--the same width as the slot, then stick it through the slot and adhere it to both top and bottom of the needle plate. And do it for both the north and south sides of the slot. Hopefully you can get the tape taut enough that it creates a smooth surface without collapsing into those crags. Then (in theory) the thread will have nothing to get caught on.
I should point out that my suggestion is pure theory, I've never had to try this myself. But I figure, if you may have to throw this plate away and buy a replacement anyway, you have nothing to lose by trying a simple fix with common household items first.
If you do try it, please let us know how it turns out!