Yeah I don't expect they'll try to compete directly with AWS or Azure or GCP. If anything, they'll host workloads on Azure, since they recently inked a deal for billions in Azure compute.
The business model I'm thinking of is more like Deno Deploy. Runtime + serverless hosting model + (in Anthropic's case) first-class integration with Claude APIs.
There are innumerable VC-backed startups that would pay for such a service that gets their ideas up and running that much faster.