Long ago there were market hunters,folks who made income shooting game and selling it.
Market hunting was credited for the extinction of the passenger pigeon.
Wild duck and goose populations were down,the canvasback near extinction.
Shotguns weren't the cause,but the bison and pronghorn were near extinct.
Back at this time,very large home built guns called "punt guns" were attached to boats,called punts.They were nearer to artillery than shoulder fired guns.The puntswere camo'd and silently sculled up to a sitting flock of ducks,then the ducks were "claymored"
The old 6 shot Win 1897 could be used in similar fashion.
I would not say an intrusive government was behind the law.
A large percentage of folks recognized sport hunting and commercial slaughter of game are not the same.Sportsman were the driving force behind regulations to help keep a sustained population of wildlife for the future.
So,we got some weapons limits,bag limits,seasons,etc.
We also got a 10% tax on guns,ammo,sporting goods to help fund wildlife.
And concerned folks created Trout Unlimited,Ducks unlimited,Pheasants Forever,etc.
So,no,it not a plot to disarm you.
Now,please consider this:Life is hard enough for the birds and game.They catch a pellet or two in the guts,they keep flying.Maybe you notice you stung one a bit.
Those birds die.If you take three,but wound six,you kill nine,plus the chicks they would produce
Banging out five or six shots instead of one or two will not collect many more birds,but it will wound more.
If the limit is 3 birds,consider limiting yourself to 12 shells.Thats 4 a bird.It should not be a problem if you can shoot.Even 15,thats 5 a bird.By self limiting (no.I don't want a law) the amount of ammo you use in a day,you'll pass up "poke and hope" shots.
You'll cripple fewer.Let the ones too far go.Shoot one bird till its down,keep your eye where it fell,and go pick it up.
Your shotgun is lighter with 3,anyway.
Me,I like a double.