I pay nothing to BCGE, everything free. My employer has negotiated some kind of partner deal with them: I get one free private CHF account at BCGE and a free gold credit card, in exchange for agreeing to receive my salary there. It’s the weirdest banking thing I’ve ever seen, I’m in ZH and they’re in GE, and I can withdraw all my money as soon as it’s paid, so I don’t see what’s in it for BCGE… Customer base of overpaid engineers? For me it makes total sense to keep it this way of course.
But regular account price is 3 CHF/month with them as far as I can find online. Possibly free for under 25yo. So maybe a free postfinance account and tunneling the money through a free swissquote account would be cheaper
Regarding postfinance credit card - I’d recommend cancelling it and getting the free cumulus or coop card. They’re free, and also offer a small cashback in points.