I see what your saying about it running on non-electrified routes but the whole point is that it avoids the need to change trains, and lug about baggage.
In other threads I have pointed out the advantages of through trains for passengers. However, when it comes to running diesels over electrified tracks, I believe that the best use of resources overall must remain an important consideration.
Services in the Westbury–Southampton–Portsmouth corridor are very well-used; don't underestimate Portsmouth as a passenger magnet!
Also bearing in mind these FGW services are the only fast services between the two neighbouring cities of Southampton and Portsmouth.
I have seen the Portsmouth Hbr - Cardiff services are very well used so it would be a big mistake to reduce the frequency by diverting some trains to Brighton.
Trains do see to be very well used between Portsmouth & Southampton.
I have to agree with these two posts. I can't see many advantages at all in cutting Portsmouth services in order to run a couple more trains to Brighton.
Portsmouth is a useful gateway to the eastern half of the Isle of Wight, is a naval base, and is an important centre for shopping and leisure, not to mention touriism.
That's not to say that Brighton isn't, but given the resources available, it makes a lot more sense to run trains to Portsmouth Harbour. It isn't as if they are not used.