It would make sense, especially for MO, to have an option to hide migrated and on hold questions in the user preferences. Is there a way to do this already? If not I think this would make a nice feature.
I suspect this will not become an official feature but I am sure a user script could be written.
(I am unsure of how migration works so in particular hide questions which are migrated away from MO rather than hiding questions migrated to MO)