Should Two Front Teeth Crowns Be Attatched? (photo)

It is sometimes advantageous to splint teeth for strength but it should only be done if necessary.  You can floss splinted teeth but you must use a floss threader.  The temporaries look oversized, make sure you are happy with how the permanent crowns look before they are cemented.

SOMETIMES permanent crowns are attached, but usually only if there is a periodontal (gums and bones) issue or after braces (to act as a retainer).  Absent of that, it is best to have them separate.

However, 99% of the time the temporary crowns are joined as you describe.

I can see no reason to have your two front crowns joined together.  The cosmetic result will be more difficult as will keeping them clean.  It is normal to hook the temporaries together to be more secure but not with the permanent restorations.  The temporaries look bulky so I would be sure the lab is not following them as a guide to what you want in the finals.