I don't think the Gatwick Express really has premium fares as such. Normal tickets are valid on it in the same way as any other service, and indeed that was the case when it was a TOC.
There is an issue with the fares between London & Gatwick being about as farcical and confusing as you can possibly get, and the lack of an "Any Permitted" CDR (which is available from places like Three Bridges to London Terminals and yes, you can start "short"), and the new franchise is/was an opportunity to standardise that.
Many people are paying more than they should be paying for Gatwick <> London, but only in the rail industry is this seen as acceptable and a loss to the business if the overcharging is reduced or eliminated.
Yes, if you combine a premium TOC with a loss making TOC, you can reduce the loss, but would would happen anyway without combining them so my understanding is this wasn't the reason for the single franchise. The main reason was to make better use of paths and stock. The Government wanted (and perhaps still want) to completely eliminate the Gatwick Express but there was a lot of opposition at the loss of a service that was aimed at a minority of the market.
The reality is that these trains carry many more empty seats than full seats - except of course at times when they run through to Brighton! You can very easily get a coach to yourself on most trains.
The service is in a state of limbo while the Government can't really decide what to do with it. So the wasting of paths, the ludicrous crossing over multiple lines at Gatwick, the fresh air being carted around, the passengers being ripped-off, and the poor platform utilisation at Gatwick, all continue for now.. except at peak hours.