I see BSO freewheels wobble slightly all the time, mostly because the lube has dried up and things at the cone/race are opening up, but nothing to concern over, afterall, it's a BSO that will be used a total of 3 hours a year.

As long as the RD still works, the FW is fine for the BSO. Afterall, it's a BSO that will be used a total of 3 hours a year.

By the time the FW is totally shot and rear shifting goes wonky, no owner will bring this to a LBS for repair. The BSO at this point has a whole lot of other problems like loose cone nuts, bent rims, missing spokes, seized seatpost, seized quill stem, seized brake/shift cables, totally rusted chain, loose headset.

It goes to the curb for the next lucky DIY that can learn how to restore it.