If you want to get real BAT that you could send to any address, send to Uniswap, or cash out, you must create an account on Uphold and complete full KYC before you can withdraw. That's when, invisibly, the IOU BAT becomes functional, cryptocurrency-like BAT.
It's like there are 2 BATs in reality despite the marketing. FakeBAT and RealBAT. FakeBAT only works within Brave's approved creators and is what you receive in your browser, and you can convert it to RealBAT which is on Ethereum and ERC20 compliant but only if you do KYC.
And, you might be OK with that for what it is, and might not want money laundering. Fine, but don't advertise it to me as an extension of a privacy browser. This is perhaps the least private cryptocurrency ever outside of USDC.
It's entirely possible to trade bat for many other coins on exchanges without KYC, but Brave forces you to be unable to do that (regardless of your local laws it seems?)
This is something Brave could easily fix by just exposing an API to allow you to do what you want with your BAT instead of forcing you to use a third party KYC service.