And the funny thing is those extra checks won't stop someone travelling from say Newhaven (or another station out east without barriers) towards a station out west without barriers as they will simply buy a London Road - Hove day return to bypass the checks at Brighton
They may do though, because if conductors have been briefed to do more ticket checks at any point during journeys, which really could happen at some point on the way into Brighton, that will be a case where you are caught red handed on the train, and depending on how nice the guard is, you'll end up with a penalty fare or having to pay the fare you should have paid in the first place (maybe if you claim you couldn't work out how to use a self service ticket machine). While I see your point, the ultimate reality is that the stations out west which do not have ticket barriers are generally the kind of stations which have lower passengers, who mostly tend to go only into Brighton itself, so I suspect journeys from say Fishersgate to Newhaven are probably pretty rare, at least in terms of commuting.
Overall, I would say that a hypothetical solution rather than all of this nonsense happening would have been if all conductors are asked to do a full ticket check (to the best of their ability) on the first leg of journeys out of Brighton, so for the West Coastway line for example, that would be between Brighton and Hove. Likewise, the instruction could be to do it on the last leg of the journey from Hove to Brighton for services arriving into Brighton. That way, they could ensure that everyone has the right ticket coming into Brighton for the automatic barrier, and if someone gets caught red handed at the barrier, then let normal staff deal with that, given that could technically happen at any railway station in the whole world which has ticket barriers. Too much of the time, I have seen guards just sitting in the back cab, and getting them to do more I would say is reasonable, particularly given they striked to keep their place on the railway in 2016.
Looking at that job description, I think its absolutely hillarious how part of the job is apparantly to ensure "outstanding" customer service, despite the fact that making it harder to interchange at a key junction and berating passengers who attempt the convenience of just walking across the concourse straight from one platform to another really isn't good customer service by any stretch of the imagination.