I don't disagree that shooting one gun for everything would make you more accurate, but i believe the loss in comfort caused by shooting different guns is outweighed by the ability to shoot guns designed for that purpose. For instance, I dove, quail, pheasant, rabbit, and squirrel hunt with a light weight 2 3/4" model 12. I like that gun and I feel like I shoot it better than any other gun I own. BUT, in January in a duck boat when there's going to be ducks and geese mixed with mud, ice, water, wind, etc that Model 12 simply isn't as good as my 3" BPS or even my 3 1/2" 10ga BPS. What I lose in accuracy I make up for by having a gun that can get wet, scratched, frozen, etc and still function flawlessly plus shoot the larger shells. Now when spring comes around could I shoot any of those guns at turkeys? Sure I could, but I've got a gun that's better for turkey hunting than any of those mentioned. (Besides, if you miss a turkey with a shotgun it's not the gun's problem).
To me the question isn't "can you do everything with one gun?" clearly you can. But I'm pretty confident in saying that just because you CAN do it doesn't mean it's the best idea.
Of course all of this depends on exactly what you're going to actually hunt/shoot.