Ignoring for the moment that Cantabrigian's post is, in and of itself, cause for incitement of a riot ...
In my opinion, and to paraphrase another poster, I think the history and working method of a craftsman will eventually lend themselves to become a 'house style', though I also have to admit that to recognize such characteristics requires the eyes of a connoisseur.
House style is more commonly associated with tailoring than shirtmaking. That aside, I would agree that the vast majority of shirtmakers have a particular type of shirt which they prefer to create. However, the more common elements which are normally associated with the phrase "House Style" do not apply to shirtmaking. These would include silhouette and construction. Here one needs look only at the extremes: mildest suppression/soft/A&S vs. sculpted/hard/Fioravanti. That which falls inbetween yields what is considered to be the house style of all the other tailors.
Switch to shirtmaking. Shirts basically conform to the body. Hence, silhouette is God-granted, not tailor-created. There is no such thing as hard and soft construction in the majority of the parts of a shirt body. The shirt is only as hard or soft as the fabric from which it is cut. We don't have the luxury of the use of padding, wadding, canvas, and thick cloth which makes tailors' lives so easy. (Yes, I'm ducking now.)
Yes, I grant that there are hard and soft collars & cuffs. And I grant that there are slightly fuller and slightly more tapered bodies. But in the main, these are preferences expressed by each individual client and (hopefully) adhered to by the shirtmaker. Of course there are instances such as T&A's 3-button cuff, Charvet's gussets, and Arthur Gluck's collar shape which could give rise to the concept of a house style. But I make 3-button cuffs, have no quibble with Arthur's particular collar and ... well ... gussets ... uh ... goshdarnit. I just can't go quite that far.
As close as I've ever gotten to a house style is that number of clients have liked my personal dress collar and I have replicated it for them as well as a few who have asked for the Joelle cuff and gotten copies. Aside from that, my only claim to a house style would have to be that I won't use gussets.