There are several use cases for youtube:
- User connects with an account (your case)
- User browses anonymously (my case)
As a connected user, you'd think that it would be more practical to store settings with your account. But this would prevent these kind of settings for unconnected users.
If setting are stored in the browser, the functionality covers the needs of all users, whether connected or unconnected. There is a drawback that connected users have to redo setting several times. But I suppose that most users would probably use only a couple of devices, so that the local setting does not impact fundamentally their browsing experience.
Of course, one could argue that it should not be too complicated to let the two approaches coexist. I can hardly imagine that the additional processing of this synchronisation would overload youtube's servers. So there might be a non-technical design decision on top of technical simplicity.
A final remark is that the local setting favours the default setting. The question is then whether or not there is an interest for Youtube in the default setting or if there are use cases that would make the one more comfortable than the other. I think that youtube has the means for doing enough behavioral studies to believe that this was carefully considered and that it's a deliberate design decision.