Also, note that you are probably giving up some privacy when using these tools (although this is true by using any fiat card).
Exactly so! Have you ever wondered how these Loyalty and rewards programs make money? They are not charities that will give you a cashback on your fiat purchases! Remember, when something comes for free, then you are the product and that's exactly the case here. These companies make money on user data monetization. Do a quick google search and you will understand how deep these things run within the internet. Everything that is free in the internet that offers you rewards for free, makes money out of your data.
These programs are linking your fiat data with your crypto data which has varied use cases. Government could be one of their primary buyer if they are able to scoop up sizable amount of data. So personally I wouldn't suggest anyone to use such services if they are serious about their privacy. Otherwise, it's all fine!