I have cards that charge fees. some $500+ a year. But to be sure, That card will "make" me $2000-3000 a year in perks, rebates and credits. I pay all my cards off monthly except a few I flip around for 0% transfers. I mostly do that to keep old cards from closing. Amex platinum is worth every cent, I travel a LOT.
My go to are amex plat ( travel perks and insurance and service credit, plus amex CS is the best ), chase sapphire preferred ( primary rental car coverage, travel perks ), sams club mastercard (5% back on gas).
It's not carrying a balance or not carrying a balance that knocks you. Its changing patterns. You get "bucketed" into categories. If you normally do X and suddenly do Y banks freak out. Its also use it or lose it. You have to keep your cards active. Put some bill on each card and have it on autopay. I have ridiculous limits I almost never use and I never carry a balance except for promo rates. Once you have a history of charging and paying off $3-5k a month on a card getting absurd limits is easy. Provided you are not manufacturing spending doing some scheme. I pretty much spend all of my money on cards and take the 3-6% cash back and pay the bills in full. Its free money, a discount on whatever. If someone isn't giving me a substantial discount for paying cash, its going on a card for the warranty and protection benefits alone, rebates just sweeten it.
You buy something on a card and it gets stolen the card will replace it. They will cover you for a cancelled flight, unexpected hotel stay or car rental accident ( most cards are secondary to any other insurance, primary coverage is a rare thing these days ). Bust your cell phone, or it gets stolen, credit for a new phone if you pay your bill with card. You need to look at it like that, rather than just another bill.