Naive approach with sequence (or serial type which uses sequence automatically) does not work. Transaction "one" gets number "123", transaction "two" gets number "124". Transaction "two" commits, now table contains "122", "124" rows and readers can start to process it. Then transaction "one" commits with its "123" number, but readers already past "124". And transaction "one" might never commit for various reasons (e.g. client just got power cut), so just waiting for "123" forever does not cut it.
Notifications can help with this approach, but then you can't restart old readers (and you don't need monotonic numbers at all).