Jones, if you're thinking targets--say 5 stand or sporting clays, or even skeet if you're shooting it with a double trigger gun--being able to select tight barrel first can come in quite handy.
Bird hunting . . . that depends on species. I now live where there's a lot of grouse and woodcock hunting. I've never intentionally gone rear trigger first on a woodcock, and I can only recall doing it twice (in a lot of years!) on grouse. On the other hand, if you're a pheasant hunter . . . I don't often hunt in big groups, and always over dogs. Usually pretty good ones, mine or someone else's. So my shots may, on average, come closer than they do for other pheasant hunters. But in a pheasant gun, I like a lot of separation between the two chokes. One pheasant gun I'm using this year is skeet and full (005/035). On a pheasant hunt using a gun with just a bit less separation than that several years back, I intentionally went to the rear trigger first 3 times in a row, I think in about half an hour. Worked well on the first couple long shots. 3rd try, I was maybe a bit cocky and tried to stretch the tight barrel beyond my ability. But I find myself selecting tight barrel first relatively often on pheasants.