Sure, for example Daedalus standard wallet for Cardano. It’s a full blockchain node. Does not go through any centralized servers. You have a direct connection to the blockchain.
That is how blockchains are supposed to work - without relying on centralized web servers (which defeats the whole purpose of blockchain). If you have any real value, that is what you use. If you are a hobbyist, then a web-dependent wallet like Yoroi is fine (if we stick with the Cardano example), which is arguably faster, but relies on ‘trusted’ (i.e., centralized) servers. The point is that there should a choice. If you have small change in Anchor/Terra, use the web-based access/wallet. But if you have real money in, use the full decentralized wallet.
There would be no site to trust then. You get a legitimate (always check the checksum when downloading, before installing!) copy of the latest full wallet, install it and run it. It should be up on github and other sites for download. Not difficult to verify authenticity of the download.
But failing that, at least there should be multiple front-end sites for the web ‘dApp’, until there is such a fully functional non-centralized wallet. As for what to trust, it would have to be community based, where you put your trust where there is enough critical mass using it, and where others have audited the code that it runs and confirmed that it is the proper code without any backdoors or such inserted.
And yes, all of DeFi, that runs on web ‘dApps’ (vs. full direct-to-blockchain wallets) has a problem. How it is now, it practically bypasses the decentralizaton of blockchain. The chain can be decentralized to the infinity, but if the only access is centralized where one party is in control (so it can be taken down, censored, and also an easy target to hack), well, that is the single point of risk and failure. IMO for dApps that don’t involve real money, such web access is fine. But for anything involving real money, there needs to be a full blockchain wallet/app, which interacts directly with the chain and doesn’t rely on centralized servers.
Edit: or at least support in third party wallets. TFL really should pay Ledger to add full Terra + Anchor functionality in the Ledger Live app (it’s not like they’re short of money). That would give an alternative to the current TFL-controlled front-end, at least for Ledger users.