How PoW blockchain can stop split-view attack (or at least make it very expensive)

Clients should expect hash codes from miners in certain time limit. This way they can assure a network of miners at international scale has answered it. (Not a local weak one)

Beside what if targeted clients of malicious ISP start mining. If ISP send them fake block headers he have to pay them mining reward, too from its own pocket
The newer PoS blockchain can not offer any of these (tell me if I'm wrong)
It is useful for certificate transparency, binary transparency, and I think it can be used for content transparency (for content available only in login areas)