I'm not convinced the extra fee is worth it, but I don't typically do cashback but award points.
My state does not charge any convenience fee however which is a huge benefit!
Any benefit from regular award points would be marginal at best.
I suspect OP is taking about meeting minimum spend for signup bonuses. Example: Get a new Chase Freedom. Spend $500 in the first 90 days of card ownership and get $150 worth* of points.
Presume 1.9% convenience fee, and you're paying $9.50 to get $150. If the card is used as a 1% back card, you're paying $9.50 to get $155. If you add an authorized user, it's now $9.50 to get $180.
Alternately, spend on whatever the rotating bonus category is, and you are getting $200 for $500 in spend.
The churner will then cash in the signup bonus and either "sock drawer" or cancel the card. Serious churners will be running lots of cards.
If you want to try this, here's my referral link:
http://emailoffers.chase.com/T/v200000159d236c463bd28776e96189988/b3779b730f3445f00000021ef3a0bcc6/b3779b73-0f34-45f0-a02e-6426ae2bdd6aChase is a good place to start first - they will only give you a new card if you have LESS THAN 5 new cards (from any bank) in the past 2 years. While some might tell you to start with a premium card, the commitment is higher**. I think this is a good starter card.
*If cashed directly. If you want to use it on travel, you can get higher value - especially if you route the points through a premium Chase card...
**Example, the Chase Sapphire Preferred. $550 for a $4,000 spend and adding an AU. Annual fee waived the first year, $85 after that.