Sending headers earlier than the normal course may have far reaching consequences. Below are just a few of them that happened to come to my mind at the moment:
While current PHP releases may have output buffering on, the actual production servers you will be deploying your code on are far more important than any development or testing machines. And they do not always tend to follow latest PHP trends immediately.
You may have headaches over inexplicable functionality loss. Say, you are implementing some kind payment gateway, and redirect user to a specific URL after successful confirmation by the payment processor. If some kind of PHP error, even a warning, or an excess line ending happens, the payment may remain unprocessed and the user may still seem unbilled. This is also one of the reasons why needless redirection is evil and if redirection is to be used, it must be used with caution.
You may get "Page loading canceled" type of errors in Internet Explorer, even in the most recent versions. This is because an AJAX response/json include contains something that it shouldn't contain, because of the excess line endings in some PHP files.
If you have some file downloads in your app, they can break too, because of this. And you may not notice it, even after years, since the specific breaking habit of a download depends on the server, the browser, the type and content of the file .