I know a lot of people here dislike Ethereum, MetaMask does have a feature of potentially showing a warning if the user opens a phishing site, which I don't think uBlock Origin has that feature.
Trustwallet and some other wallet that I can not point to people to use also have that, but I do not think it is working in a way that it is pointing to phishing sites, I think it is pointing to new created sites.
I have seen new created legit site for presales that would be first tagged as 'may not be legit' on these web3 wallets, but legit. As the site grows older, the warning message will not appear again if the site is legit.
But why should wallet become a browser? That browser called web3 is now majorly used by scammers to make novice to connect to their fake website, we can see people complaining everywhere and including some member on this forum about their wallet that they connect to fake website and all their money stolen.
Metamask is not a shield in anyway. If you have your coins there, there would not be warning if a hacker have access to someone's metamask wallet and know the person seed phrase or able to transfer the coins on it. Metamask can be as vulnerable as other online wallets.