A 30" bbl on an 870, for example, is already a very long gun and puts the front bead almost as far from your eye as a 34" break-action gun. A 36" bbl would likely swing like a telephone pole and could be rested on the trap house roof
Keep in mind that a pump or semi-auto has a receiver that is typically about four inches longer than a break action, effectively giving you a sighting plane that's about four inches longer than the barrel length.
So a 28" barrel is equivalent of a 32" break action barrel, and a 30" barrel is equivalent of a 34" barrel. So a 34" pump barrel is going to have a sighting plane of a 38" break action barrel, plus a lot of extra weight (about 6 to 8 ounces). This is why they are not popular.
If you want a heavy gun with a heavy barrel and to balance it weight in the buttstock, so as to reduce felt recoil and slow down and smooth movement, or you want a rock steady gun that you don't move much for caps, then a 34" barrel might work. You'll find it won't be of much use for singles and doubles, and will all but eliminate the ability to "jink" the gun in sporting clays. I tried a friend's 34" barrel with a comb that was set up to shoot a very high pattern (135%). This allowed the shooter to not have to move the gun in the vertical plane for caps. The only movement was left and right. This eliminated error caused by vertical movement, but of course required precise timing to catch the bird in the same spot in flight. The gun felt to me like it had a telephone pole on it, but it was rock steady, almost like shooting a target rifle.
Card shooters and other long range side match shooters might find a 34" barrel useful, especially if they have a tight choke or can make the choke effectively tighter by backboring.
Have seen Marlin bolt action 12ga Goose Guns show up at turkey shoots. The shooters did quite well with them.
I've wondered why at the height of the turkey hunting craze that Marlin did not bring back their 12ga Goose Gun and equip it with rifle sights and drill and tap the receiver for a scope base. They've had one of the best turkey guns ever made and didn't do anything with it.
There was a Gentleman who shot on my squad at the grand. I 'm not sure but I think it was 1991 or somewhere in that area but He had an Rem 870 with a 60" barrel on it. I thought I had seen everything but that took the prize. He even got a photo taken for Shotgun Sports. His score weren't great but the gun was impressive.