A running toilet is usually a flapper or a fill valve and it is a small repair that wastes a considerable amount of water. A toilet that rocks is a different matter, because movement breaks the wax seal and lets water seep into the subfloor where nobody sees it.
That seepage is how a rocking toilet becomes a floor repair. If yours moves when you sit on it, it is worth pulling and resetting before it damages the subfloor beneath.
Flange repair is the common finding once a toilet is pulled in an older Wichita house. Cast iron flanges corrode and break, and the fix is straightforward but it has to be done properly or the toilet moves again.
Technician insight
A toilet that rocks even slightly is breaking its seal every time it is used. That is a subfloor problem waiting to happen, not a comfort issue.