I don't think that is meaningless. Of course you have to compare the previous block hash included in the first block of your chunk with several sources (e.g. at all block explorers you know if you're paranoid 
). But if you know e.g. that you received a Bitcoin transaction one day before, but want to check the correct amount without having to fire up a SPV wallet (which potentially may expose you to Electrum server privacy attacks) then such a service may be quite neat as you can check all blocks of the last 24 hours approximately. You do all the analysis on your own device, without exposing the addresses you own, and without needing a full node.
You need to know the exact block hash to download, and having the block itself doesn't provide any form of security, which is why SPV wallets require at least the block headers. Having the block headers still doesn't give you any good information about the required transactions. This means that you must know which are the blocks to download, which means you also have to trust someone to tell you the exact blocks and download those. In essence, I'm describing an SPV wallet; its probably easier to use an SPV wallet and start querying random addresses to obfuscate your actual address. ). But if you know e.g. that you received a Bitcoin transaction one day before, but want to check the correct amount without having to fire up a SPV wallet (which potentially may expose you to Electrum server privacy attacks) then such a service may be quite neat as you can check all blocks of the last 24 hours approximately. You do all the analysis on your own device, without exposing the addresses you own, and without needing a full node.Also if you want to do some onchain analysis of certain blocks on your own (e.g. to look for hints which addresses could belong to a single wallet) and you know approximately the timeframe where you're searching, that would also be an use case for such a service.
In the end, that kind of service could basically enable everything a normal block explorer can (even what walletexplorer.com does, i.e. search for "connected" addresses which may belong to the same wallet), only that you need slightly more resources on your device, but far away from the resources you need for a full node.
If you want to index all the transactions, you need a full node. If you only want to know a subset of them, you need to get your information from someone that is running a full node. Else, you would be randomly searching the blockchain, without any validation which opens you up to a host of eclipse and sybil attacks. There were several wallets which implemented BIP157 and BIP158 which supposedly provides more privacy than an SPV wallet.In the end, that kind of service could basically enable everything a normal block explorer can (even what walletexplorer.com does, i.e. search for "connected" addresses which may belong to the same wallet), only that you need slightly more resources on your device, but far away from the resources you need for a full node.