The server spec is for a general purpose HAF node that can store all the blockchain data. In a couple of weeks we'll have support for operations filtering (i.e. to filter for only the operations your app is interested in), which will make it quite cheap to be able to run an app-specific HAF server.

As to public servers, I'm sure there will be some, but you would need to get agreement from the server owner to run your app there. And for development itself, you're going to want to run your own dev server. So you may need to wait till filtering is implemented if a server with 4TB worth of storage is out of reach for you.