It won't work because the ListView webpart uses the GUID of the connected List, and the Views are stored in the List configuration.
On another site, it is another List, with another GUID
So you have to migrate the List (it will include all its Views) by saving the List as a Template, not the ListView WebPart
(you still need to recreate the ListView WebPart then, and connect it to a View)
If you are doing large scale deployments look into PnP:
If it is just a handful of ListViews, you are faster just recreating them by hand.
A long, long, very long time ago I wrote a Bookmarklet to add Drag & Drop to the ListView Edit page, that speeds up configuring Views: