Wal, Briley does make the insert you mention and the reviews of it I've read do make it sound as if it works quite well. In fact one review in a shotgun magazine I subscribe to says it actually got MORE velocity from the larger barrel with that insert than in a .410 barrel which just blows my mind and that patters were at least equal to the standard .410 barrel.
Now to say it's taking the nation by storm would I think be a bit of an over statement. I can't imagine trap shooters falling all over themselves to use a .410, not even from the 16 yard line.
BUT skeet shooters sure are loving it these days. I'm not even sure just what has happened to the .410 in recent years but for sure it's more gun than it used to be or so it seems to me. Back in my competition days I did good to stay much above 85% with it, don't think I ever reached 90% with it on my best day. These days I'm shooting it pretty much the same as my other guns and in fact the last time I shot both it and my favored 28 ga I actually did better with the .410. Now that wasn't one of my better days over all but the .410 sure was a bright spot in the day. I think I broke 45 of 50 with it that day which is far better than the best I ever did in my competition days with the .410.
These days at most any big shoot it takes a 100 straight to win the .410 gun championship. Back when I stopped shooting competition I think there had been fewer than 20 perfect scores ever shot with it and only a handful of guys who had ever done the deed.
Heck I'm smoking the targets with mine now and even at times have smoke hanging in the air from breaks from stations 3,4 and 5 as well. I sure don't know what's going on with the little gun but it's better than it ever was these days.
I shoot a Browning O/U with Briley skeet choke tubes in it, not the short things you're talking about. It's a .410 bore gun but with Briley screw in choke tubes marked skeet.