I have a kitchen table that has some of the finish rubbed off.

I would try to remove the formica to get to the wood. Hopefully it's decent looking wood. If not I would paint it. I've also seen projects where a new tabletop is made and it fits right over the old tabletop. Just a 2x4 frame for underneath the new tabletop that is slightly larger than the old tabletop. Once the new wood is attached to the top of 2x4 frame, the whole thing slips right over on top of your old table. Bonus - it could be removed for crafting, kids coloring or painting. Slip it back on when you're done. No damage! Search for "tabletops" and you should find some.