Markup in plain text field not getting processed

Problem/Motivation

The Freelinking filter doesn't appear to work under the Plain Text format; I can enable and configure it in the configuration for Plain text, but viewing a page with a Plain text textarea containing Freelinking markup results in the untouched markup being displayed.

It does work for me when using the Basic HTML format; and putting two textareas on a content type, one Plain text and the other Basic HTML, with the same text and markup in both fields results in the Basic HTML one getting the markup transformed to links as expected, while the Plain text one is displayed with unprocessed markup.

To reproduce:

1. Add two textareas to a content type, one with the Plain text format and the other with Basic HTML;
2. Add some text with valid Freelinking markup to one of the textboxes and copy/paste it into the second;
3. Save the page and view it or click Preview