Usually I can use Q to place an entity the same as selected but "edited" inserters they are placed in their default state. I can copy it with Shift+Click but for inserters I expect them to be copied automatically.

Make sure you're not over-writing the setting with the pre-place menu. it overrides all inseters placed by the player.

This might be a dumb question, but how do I do what you suggested?

the pre-place menu is in the top left corner, a menu opens when you click an inserter button.
if any checkboxes are turned on, you're overwriting the defaults.
the settings don't go away just because you closed the window.