Actually it's a great way to simultaneously design a website AND an api for others to use. It's also a great way to separate concerns. It's also a great way to reduce load on your server. In fact, it's an easy way to have some people code a standard back end with a standard authentication so that some other people can make front ends for the web, iphone, and more. You can use, for example, oauth to authenticate with the back end, from any front end app.
I dont't think we are quite on the same page, having an public API etc is wonderful but let's use a slightly different topic. Using some 3rd party ORM to talk to your database is generally a no brainer, but v0.1 might not even have a database yet because persistence is not generally needed for a demo. Why put off such a core feature, because just changing your objects is less friction so and the goal is to see if anyone is ineested. aka idea validation and nothing else.
Because it's just as easy to code your front end independently and then hook up your back end to it. If the front end is static, it can be completely hosted on a CDN. If your back end is unreachable the front end can just take another code path. There's your 0.1
http://www.discourse.org/ is one example of such an approach