My view is a little different.
Dog's aint children. Humans, even kids, will always have higher intelligence than dogs.
So, if you've got a gundog then it's a pretty safe assumption that it was bought for hunting.
What has teaching a gundog not to take washing off the line got to do with hunting?
I prefer to concentrate all my dogs teachings along hunting related lines.
Different if you're teaching a dog not to break/grab quail or some such, but washing on the line really has nothing to do with hunting. So why fill the dog's brain with non-hunting related teachings? I prefer my dogs to think of nothing but hunting related thoughts.
Far easier to just take the washing off the line before letting the dog run.
If the dog is running & the washing needs hanging out - put the dog away.
Problem avoided altogether.
Yeah you can teach the dog not to grab the washing, but just what if.......???
Suddenly we end up with a problem to fix that has absolutely nothing at all to do with hunting.
Why allow the chance of that problem arising, to surface in the first place?
As you said - an ounce of prevention.......
Just keep the washing & dog seperated. No problem.
Washing out - dog away. Dog out - washing away.
No problem to have to fix.

Chooks are a little differnet. I see them as a positive.
They are birds. Brittanys are bird dogs.
Teaching not to touch chooks can have a positive effect on bird hunting/handling for the dog.
But washing??? Never shot a shirt before