I think it makes sense to do this, mainly because Bitwarden's official server is AGPLv3. This'll help avoid conflict between the two.
I doubt very very seriously that there is overlap between the audience who runs Vaultwarden and those who want to start up a company that sells Vaultwarden as its backend to compete with Bitwarden
Company selling password managment as a service might use the code to give their customers migration path to their service
Can't be worse than LastPass tho.