That's inaccurate, orbital periods are a thing at least for moons. It's one of those things you'd have to spend a year or two piloting an Orca to notice though.
if anything, people DON'T want them to move because it will ruin their bookmarks over time. It is not going to be fun to have to manually update your bookmarks just because a space station got slightly pulled into some nearby planet or whatever.
I mentioned this in another comment, but if they moved you would have to manually update bookmarks to warp to those locations as they drifted, annoying.
You would not need to update any bookmarks. They should be using a coordinate system based on a relative object. Existing bookmarks are already technically relative the largest gravity well. New bookmarks would simply be based on whatever you want like any object. Absolutely no reason to overcomplicate it. Dunno why you're assuming you'd need to update anything.
Ok, lets try one example, the game has a mechanic where a station has a docking port where all ships exit oriented in a single direction. Many pilots have bookmarks that allow them warp very quickly away because turning around is slow so the bookmark is oriented straight directly away from the exit. How does one deal with that in a solar system if we assume even minimal orbital simulations?. It has 9 planets 33 moons, and only the dumb players warp directly to any particular planet or moon because of course everyone expects that, so they place them in random positions in space.
I played it for years. Shaking my head at this silliness. You just set the bookmark to a 50 meters off the side of whatever station and then the position of the station is basic orbital algebra that takes almost no CPU to calculate. It's dumb you can't just activate the warp to immediately activate for one second in whatever direction. Another reason I stopped playing. Irl you'd warp away in any direction if you're about to get blasted. You wouldn't be wasting time aligning to some random bookmark. This is why I can't take Eve online seriously. Like you actually think that a 25 year old engine is the best design ever for some reason.
Tactics like being able to have your fleet hiding behind a moon that happens to orbit into the exact right position at the right time is fun to me. Eve Online is already a spreadsheet simulator so I find it about as fun as watching paint dry. Anyway I don't think basic physics is about fun or not fun.