$rss->itemDateField is for fields and not for code! It's configurable on the module screen (default) and via API.
To do what you want, give every page in the feed the date of today, you could add a property hook to Pages.
So you can define what, for example, $page->myPubDate will return. Then use that property for itemDateField.
So such a hook would look like this, as also shown in the HelloWorld.module example. In your template code just before you render the feed:
wire()->addHookProperty("Page::myPubDate", null, "addPropertyDate");
function addPropertyDate($event) {
$event->return = date(DATE_RFC2822);
}
Now after this code a call like
echo $somepage->myPubDate;
Will return the current date.
SO later in the $rss code you can set:
$rss->itemDateField = "myPubDate";