Whatever profit Centrica make overall doesn't mean a dime to BG. Centrica aren't allowed to subsidise BG losses under the terms laid down when the monopoly was removed.
You would dispute the figures (despite the fact I've seen them with my own eyes and you would to if you bothered to look for them). And what's wrong with trading on their name? Name me a business that doesn't! If I thought I'd get something better elsewhere I'd switch in a heartbeat. But I've heard horror stories about every single one of the other companies numerous times. So why would I bother? If I don't have a problem with a company then it may well be worth staying loyal. At the end of the day the prices change that much that the cost is largely the same wherever you go.
But notice that the click energy tariffs are still the best. Have been for ages. So not that bad.