This may indeed be a valid use case, and Bitcoin fulfills it. You don’t need to build a separate blockchain, you just need to know how to embed a hash into a Bitcoin block and how to point to it which is technically easy.
Also it’s unclear how a separate blockchain with this sole function would work. You need the monetary incentive of bitcoin mining and proof of work to make the security model work so that the time stamp can be trusted. The security of the Bitcoin blockchain is not a computer science problem, it’s an economic one. That’s why the only application it works with is cryptocurrency, with time stamping being a nice byproduct.
Also it’s unclear how a separate blockchain with this sole function would work. You need the monetary incentive of bitcoin mining and proof of work to make the security model work so that the time stamp can be trusted. The security of the Bitcoin blockchain is not a computer science problem, it’s an economic one. That’s why the only application it works with is cryptocurrency, with time stamping being a nice byproduct.