How exactly would you fix a sharded cluster with bad distribution in a production environment

This may be a dumb question but this is something I have been asking myself a lot. I understand that choosing a bad shard key would result in an uneven distribution on the sharded cluster, and if you get to a point where you get stuck and cannot add more data, you would need to increase the chunk size and manually split the jumbo chunks, however this is only a provisional solution that would fail in the long term since the shard key is bad anyways. Is there an actual way to give this a permanent fix within the same collection, or you would need to make a copy of the whole collection in another cluster and make sure you shard correctly this time?

I realize it’s been a while, but for those reading this question today, according to the documentation you can now change the shard key as long as you’re on at least MongoDB 5.0.