Drywall – Taping or not unexposed wall joints

Nope. Go ahead and try it if you don't believe me! I certainly did...

The problem with wood frame houses is that they shift in weird ways as the wind hits them and as the foundation settles. The 8 foot long side of a standard drywall panel has a LOT of mechanical force to it if it moves even somewhat independently of the sheet next to it, and the joint compound rapidly turns to powder without tape to back it up. The same can happen if there is too much or too little compound or the compound is the wrong type, you can also see this problem.

This is akin to the reason that drywall is gypsum between two sheets of paper... All you have to do to break or cut the gypsum is to disturb the paper.

The best practice I've seen/used is to use Durabond to bed the tape, and then normal green stuff over it to feather the joint.

Personally I would not lose a lot of sleep over this. The molding will probably cover it up. If not have the contractor make the necessary adjustments. Tape would still be needed for the seam that is above the door that we can't see in the pictures. Do you feel that part of the seam was properly done? There is also an indentation on the edge of wall board for the tape that might have been easier to fill with tape instead of just joint compound that shrinks and could crack.