Uphold is not neccesary to use your BAT.
Here you have two wallets.
Local wallet = the browser rewards wallet (this is not a real wallet on the whole meaning of the word, is just a virtual wallet, any BAT in it is virtual and it’s converted to real BAT when you tip creators or it’s credited to your uphold wallet. This can change in the future).
Remote wallet = Uphold wallet = verified wallet.
Said that, you can earn and collect BAT with a local wallet, the only con is that you can only use it to tip content creators.
If you want to exchange your BAT for real money or change it for other tokens or just take them out of brave ecosystem, you need an uphold wallet.
I do not now (i really don’t use it) if using the binance widget you can exchange tokens from your local wallet, but i don’t think so.
In any case, AFAIK the team is working to have other alternatives to uphold, but that Is going to take a while, so, the best you can do is save them in your local wallet and don’t lose your seed phrase.