Create a blank page for each entity type

Like the node type, it has a page(/node) that defaults to the homepage.

The /node page is the optional frontpage view that's offered as optional config of the node module. If displays all content that has the promote field set to true. ECK entities don't have a field like that, so what entities would you show on that page?

To be honest, this sounds a bit too niche to be offered automatically by the ECK module. A frontpage view makes sense, but an automatic view per ECK entity type is really only useful on specific kinds of sites.