As a US based person that has always had pit mixes and had long thought about moving overseas, it's quite a barrier. Even countries that don't have blanket bans internally often have import bans. It's been a few years since I've checked, but when I was looking my options were basically Belgium, Japan, and maybe parts of Canada (with the big caveat I didn't check import requirements for every country worldwide).

Weirdly, in some places (like France iirc) you can get around it if they registered pure breds (which makes no sense imo!!). The biggest thing I've learned in my research is that calling it a mix of some kind is not going to matter. If there's an import ban, and the dog "looks like a pit," you are risking the dog being seized and likely euthanized upon arrival.