Now about hive health. There is this thing called Varroa and if you let the hive swarm half of it goes with the swarm and the other half stays. Varroa I mean. What is really good with swarming is that the hive now has a virgin queen and she doesn't lay eggs right away and a lot of Varroa dies off because they can't reproduce. They need eggs and bee larvae to do so. The swarm with old queen has an interruption as well because they need to build comb and cells where the queen lays eggs.
In my beekeeping years ago I kept hives healthy ( fight against Varroa ) entirely with letting them swarm.
Just to write it once again since by your writing I think you are confused...Old queen leaves with the swarm.