Individuals like Rosicky, Sagna, Walcott, etc. have been here for a very long time but none of them have carried the team during our trophy drought, I don't see how any of these players "deserve" a trophy. The Arsenal as a football club and institution "deserves" a trophy, as well as the fans that have been patient for almost a decade or so.
Players may not have won a trophy here but our club has helped develop these individuals, taken them to Europe, stuck by these individuals when a lot of other clubs would have written them off, given them a massive pay-rise and made some into established international regulars for their countries.
We have given these players a lot.