Using Cloaked Pay doesn't mean you have to miss out on your credit card's rewards. When you link an underlying funding source which earns rewards, you will absolutely continue to earn your card's standard base reward rate on every purchase made with a Cloaked Virtual Card. 

Since every transaction you make with a Cloaked card is passed through to your linked funding source, your credit card company sees a charge and will issue rewards based on their standard policy, so you maintain your underlying card rewards.