It offers to save the file again and does not give me the possibility to close the document within that dialogue.
It's not a blocking dialog, it's just a passive infobar, so you don't have to do anything with it. In the case the file was deleted, there are no less than 4 ways to close the file: the tab close button, the close button in the toolbar, the close menu item in the file menu, as well as <kbd>Ctrl</kbd>+<kbd>w</kbd>. If the extra step of confirming you want to lose your open document is the problem, it can be quickly dismissed using the keyboard with <kbd>Alt</kbd>+<kbd>d</kbd>.
But that said a "Close and don't save" option could be added to the infobar. Pull requests are welcome.
Seems reasonable, if maybe a little dangerous. I can imagine someone accidentally clicking the wrong button in the infobar and then having a really bad day, but I'm not strongly against it if people would find it useful for their workflows.