Show hunter attire is a fashion issue. Nothing else. And stock ties are out of fashion for the hunter ring unless you are in formal attire for a classic or a derby wearing a shad belly. Will a judge penalize you? No. Will you look out of fashion? Yes. And, FYI, the wrap collar shirts are lovely–convenient, simple, and cool for summer showing.
In the hunt field stock ties are worn so that they can be used as a bandage, sling, etc. The large pin it is secured with could also be used to secure that bandage or sling. It’s pretty rare for a stock tie to be put into service like this, but it does occasionally happen. At a show grounds, you’d never have this need. So there is no practical reason to need/want to wear one. Also, I’ve never heard of anyone getting stabbed by a stock pin, frankly there are about 1000 other weird bad things that are more likely to happen to someone in a fall.
Show hunters may have its origin as a place for people to show off their field hunters, but those days are long gone and there’s no point belaboring it. I show at rated shows and also hunt, and there are few things in my tack and attire that go both places except my helmet and hairnet. For hunting I use a different bridle (flat noseband and browband), a different bit (more severe for control in a field of galloping horses), a hunter breastplate, a different saddle (my show saddle doesn’t have d-rings on it to attach a sandwich case), different boots (heavier and more durable for the hunt field), a different shirt (usually a turtleneck under a stock tie), a wool vest, different jackets (100% wool of varying patterns and weights), heavier weight breeches, string or brown leather gloves, etc. I generally don’t hunt my show horses either.