There are a lot of reasonable complaints in the comments, but "you need to change your passwords when changing to this service" is actually not one. You want to do that anyway from time to time, and when you are using a new password manager is actually a great time.
If you want to change your passwords from time to time, as you say, then this system isn't going to suit you, because it only ever generates one password for each site.
You could change your master password from time to time and you chould increase the counter (which changes your password) for a given site from time to time.
