If using the statutory declaration of parentage route (instead of attending in person) the father has to sign the form in front of a notary, solicitor, magistrate, JP or similar. So there may well be a wait for an appointment with one of them, which may be far more hassle than just going to the register office.
Aren't register offices open on Saturdays sometimes? They hold weddings there on Saturdays at least, may be worth asking if an appointment is available then? DS2 was 43 days old when he was registered (legal limit is 42 days) due to lack of appointments! I wasn't fined as it wasn't my fault.
Pros to him being on the birth cert: well he is the father so should be held legally responsible for the child, it also means public records are correct, he can agree to things like medical treatment, schools etc, if anything happened to you he'd be able to live with/see his child without legal action, you can ensure he is paying financial support for his child (and child maintenance payments will not affect any benefits you get!)
Cons - Well, similar to the pros so depends what sort of parent he will be. He will be able, if he wishes, to challenge your choice of schools, medical treatment, whether you can move home (if out of the area), if you can take the child on holiday out of the UK for over 28 days, pretty much anything you decide for your child (doesn't mean he'd win in court, but stressful nonetheless).
If you're happy that he won't be obstructive in a way that will actually damage your child physically/emotionally, I see no reason not to put him on the certificate. It is extreme to leave him off, though some do this for very good reason. If it's just the benefit thing, don't worry, it won't affect things at all if you're not living with him now.