To the best of my knowledge A&S and Mahon both cut straight coats. To cut a straight coat there is less cloth on the front edge and more towards the chest. The front balance is also longer. The idea being that the coat swings open and drapes at the front scye, ideal for a soft chest.
A crooked coat, (the way I cut,) is cut to close, the button is there merely to fasten the garment. When unbuttoned the hem of the coat is parallel with the floor.
When buttoning a straight coat, it picks up the foreparts and creates that drag seen in the images provided.
When cutting a sloped shoulder and then putting that on a wear with a high shoulder issues can arise across the shoulder plain, as there is neither muscle nor tissues to take up this space.
The A&S look is not for me though I do appreciate the effect it achieves and as a true bespoke tailor offer that option to my clients.
For novices and idealists the easiest thing to do is critic others work. Tailoring is a tough game! During my time I have seen the strangest defects that any body has to offer. In order to achieve a really clean fit one must first opt for a crook coat, so there is no dragging at the button, accept his shoulder slope for what it is and cut according and be prepared to pay a high price, so the cutter/ tailor can afford the alterations bill to meet the clients expectations.
Cloths are lighter now than in my Grandfathers days (1896 - 1989), I'm not making 20oz wools which are tough as old boots and forgive even the grievous sinner. They are lighter weight and have to be tailored more delicately.
When it comes to shoulder padding its the back that it helps more than the front. A thick shoulder pad will lift the cloth giving more cloth across the back and cleaning the back os scyes.
Personal I use wing pads in some of my coats especially if the client is hollow back there. There is only so much one can draw the back armhole and pick up the shoulders before incurring other issues, particularly with light weight wools.
I have high shoulders so I use a 1 ply pad, once the shoulder angle is greater than 2 3/4" I use a 2 ply pad, when the slope is greater than 3 1/4 I'll use a 2 or 3 ply.
I wonder how many contributors to these posts who have read "The Art of Garment Making", or "The Science of Pattern Construction for Garment Makers", have actually cut a pattern, made a coat, put on the wearers back and had it hang flawlessly. Believe me no tailor have ever set out to make an ill fitted coat.