I think this has been asked for since the beginning of time, but not sure if we actually want this. After Julian added the code to allow File Browser to be a child window always on top, doing so for new windows created with SCREEN_OT_area_dupli ("Duplicate Area into New Window") is a trivial change.
It certainly makes the feature usable on Windows, since your newly-created windows no longer dive under the main one. I realize that other platforms might have window manager features that get around this.
But windows like this, including File Browser, cannot be individually minimized - that just isn't something that can coexist with "always on top". So this could be much better in cramped screen conditions where not overlapping is required, but the lack of minimization might be missed where there is more space when using multiple monitors.
I am assuming that this "is dialog" behavior has been tuned to work nicely on Mac and Linux, so can't think this would have negative affect there.
Following shows a torn-off window overlapping the main one, even though it does not have focus. The secondary one does not have “minimize” option. Tasktray shows only one icon that you can use to minimize them both at once.