I'm interested in where you retrieved your statistics from?
The only 2.5% cash back card (on everything) with no AF I've heard of is the USAA Limitless... And it was available in select states, required a single direct deposit of $1,000 or more a month, and also no longer exists.
If you want 2.5%+ back in rewards on all purchases, one would have to get a Chase or AMEX and redeem for flight mileage.
If you get the Bank of America Premium Rewards card and keep some level of investments (does have to be cash) there then you can get 2.62% on everything. I keep some shares there that I never intend to sell. It has an annual fee, but I think there is a non fee version now. And you get double the rewards on food and travel, iirc. And it is cash back, not miles.
I use the Apple Card for the 3% on everything apple though.