IMO a weatherbar on the bottom outside edge of a front door looks perfectly normal. Only if the door is in a deep porch and protected from wind-blown rain would I omit it.
Your door manufacturer might offer a high-tech draught reducer, but if not, get a brush pile one. Ask if they can fit it into the bottom of the door where it will not show. Common ones fit on the inside face of the door which is less elegant. The gap under the door needs to be big enough to accommodate the sagging that will take place. If it is excessive you could ask for the threshold to be built up.
Ask how they managed to make a door and a frame that did not fit each other.
Express disappointment that they intend to rectify the poor fit by adding strips to the door (if it was me, I would prefer to build up the hinge side, which will be looked at less, and will not have people brushing into it and knocking it).
Make a point of running a 2p piece all the way round the door to see if the gap between door and frame is that size, and even. (a 10p piece is the greatest acceptable gap) and do it whenever the supplier is watching you. He will think that somebody who knows about joinery has advised you. He might try to tell you they have left a bigger gap for the thickness of paint, but if the door is already painted, that won't wash.
I would probably accept a rework of the existing door, but I've never paid thousands. At that price you are entitled to a perfect job. Warn them that you expect the door to be perfect when it is returned to you. I imagine they have already lost all the profit on the door by having to come back twice.
The supplier should know, without you having to threaten him, that your next step would be the Small Claims Court.