Adam,
Just because you should not 'expect' traffic info, it does not mean you will not get it. The sentence you quote suffers from the nuances of written and spoken English. 'Expectation' implies that all traffic should be called out to you. MATS part 1 states that if there is deemed to be a risk to a flight, then that flight will be warned.
You do not have to have any service at all in Class F or G, but common sense states you do take one. Why? so you can be warned if there is a hazard to your flight.
That's what a BS is primarily there for. Alongside the BS, TS, or DS you get an Alerting Service (for free). If you do not make yourself known, then the ATCO will not transmit information that is not perinent to aircraft he is talking to... therefore you may miss some info that could impact your flight.
Your statement
No matter how you slice this or interpret this, this is the achilles heel of this system. There seems to be zero need for BS. Either remove it, or upgrade it so BS = TS.
Shows a lack of understanding of what the LARS and ATSOCAS system is about, and how it works. There is a place for BS within the system. Maybe a visit to an ATC unit will enlighten you (as far as I'm concerned it should be mandatory in the PPL).