I see no difficulty in implementing this.
When checking if a name is taken, check if the group that has already taken the name has 0 members. If that is the case, let the new group have the name.
"If someone wants to shut down a group, remove all members, and lock it, they are allowed to do that. They paid the 100R$ to buy it and it's their property."
No, once they leave it, it is no longer their property.
Anyway, I half support. Don't delete the groups, but rather allow them to be claimed. Deleting them could get rid of a part of Roblox history (or something like that), and would generally cause more complications than if we could simply claim it.