Interest is the whole story
A card's headline rate is quoted per year but charged per day on the balance you carry. That single mechanic explains why a balance grows faster than the percentage feels like it should.
Everything else — rewards, fees, promotional offers — is secondary to whether you carry a balance.
Rewards versus debt
Rewards pay a small percentage on spending. Interest charges a large percentage on debt. If you carry a balance, the interest almost always wins.
The pages below show the arithmetic rather than asserting the conclusion, because the comparison is the useful part.
Repairing credit
Payment history and time are the two inputs you cannot shortcut. Secured cards, utilisation management and disputing genuine errors are what you can do in the meantime.