I don’t see a reason to use Screentime passwords at all with Stolen Device Protection as it stops the entire mechanism thieves were using to change the Apple ID password.
The only way thieves could change the Apple ID password would be to also kidnap the phone owner so that they could use Face or Touch ID to change the Apple ID password even with the 1 hour delay.
There is a slight danger to enabling the stolen device protection, in that if TouchID or FaceID doesn’t work, you are effectively locked out of doing a lot of security related things on the device. I know my Dad’s TouchID doesn’t work in wintertime for some reason. That’s less of an issue with FaceID, but if the person gets into an accident or something the phone could become unusable.
Presumably stole device protection is enabled on a per-device basis so it would still be able to do some account related things on another device.