I learnt about payment processors when I tried to understand how some countries adopted crypto currency and use it for payments after they concluded their transactions. At least that is the only reason I know why it exist unless I get proven wrong by someone with more information. Perhaps you can explain more for me.
Which country are you referring to? Are you suggesting that some countries set up their payment gateway for crypto transactions? I never heard about that. As far as I know, most of them regulate how the payment system works, not necessarily operating it on their own. I also think you misunderstood something here since the payment gateway and exchange wallet or self-custodial wallet are different. CMIIW.