Yeah IMHO setting up the TOTP on multiple devices is a good idea. I also save the setup key along with the recovery codes so that I can easily set up new devices if I need to (plus I have seen some cases - ie Facebook - where the recovery codes don’t work). I guess this is marginally less secure than storing just the recovery codes, because if someone finds my backups they can now generate infinite tokens, but if that happens I probably have worse problems to worry about.