As a project admin, why don't I have permissions to the wiki?

Most likely, your site was installed before TeamForge contained the wiki component.

When the wiki was added to TeamForge, it was decided that there was no way for us to know the security requirements at customer sites, so permissions for the new wiki component were not assigned to project admins by default. As a project admin, you can alter any existing role to grant this permission, or create a new role for this permission and then assign to the appropriate project members as needed.