AAS could offer whatever they want to BA, the thing is would BA take them up on it and what would they want in return. Having flown both for AAS and a BA subsidiary company in the past I can tell you that BA does not do favours for other companies and would want/need to see a significant financial benefit before they were remotely interested. AAS are going to need all the revenue they can get to make the jet pay, never mind diluting revenue by code sharing.
I lived on Guernsey, like the place and all that but let's be brutally honest the traffic just isn't there. If it was the likes of Ryannair would be interested and they're simply not. As far as monopolies are concerned the market simply isn't big enough for multiple operators to Guernsey on a regular basis. Don't be fooled by talk of LGW and slot costs. If it was truly profitable for FLYBE somehow they would continue the route.
The same, frankly, is true inter-island. Whatever AAS's faults and believe me I used to moan about them in the crew room, the Islands have had a superb service over the years under AAS's various owners. I also used to fly for Air Sarnia. We couldn't really compete on service and the company went bust trying to compete on price. It cost AAS a small fortune in lost revenue when A/S was operating and at the end of the day I'm not sure that Alderney in particular benefited much. What it did prove was that there were only a finite number of people who wanted flights and even give-away prices didn't generate a significant increase in traffic, at least not enough to cover the reduced revenue per seat due to lower fares. Having multiple operators on a route may be great for the local consumers in the short term but probably isn't beneficial in the long term. The term 'life-line route' implies there is a social necessity for that route and social necessity doesn't necessarily equate with an operator making a profit. In fact generally speaking it means that somebody has to subsidize the fares. AAS did that for years on the ACI-JER route but eventually had to drop the route once Blue Island came along because competition on the GCI-JER route meant lower revenue. In that instance competition very definitely did not benefit the ACI consumer.
Competition may well act as a spur for an operator to get its act together whereas a monopoly might make them lazy but if costs have to continually be driven down to maintain profitability eventually something has to give. If the market is big enough then another operator will step up to the plate. In the case of GCI there probably has to be a near-monopoly at the very least on some routes least so it's better that a local airline which understands the social need for the route has it.
Should the States own AAS? Well the States are or should be acutely aware of the need/benefit of air links. A private/public company might exclusively focus on the bottom line, presumably the States do not because they understand that other operators are not exactly fighting to get on the Island routes. That doesn't mean they can bleed money of course but perhaps the GCI taxpayers derive more benefit from AAS than what it costs them individually in terms of their tax pounds going to AAS. I'm sure somebody will have the figure to hand. How much per year does an individual taxpayer contribute? Now what value would you put on the benefit of a regular service operated by a company that has always done it's best for its local customers?