automatically add & remove pages from the sitemap (not only add them)

Request:
Ideal would be if the component could crawl the site and update the sitemap on regular bases. And with update I mean add & remove pages from the sitemap file(s)

Current situation:
To have pages removed from the sitemap file I have to visit the server through ftp to delete the file first, then regenerate it.
I don't want to bother my client with that, it should be available from within the website.

The support team said:
An auto-crawler feature is provided and a sitemap cron feature will add new pages to your sitemap.
Normally when you add pages to your sitemap you won't have these removed, this is why initially you would firstly generate it manually and in time newly pages would be added."

My argument:
This really depends on the type of content on your website. For example a recruitement agency, they show job vacancies on their website. A certain job is only shown for the time it is vacant.