I agree that traps should be checked every day. I think the law requires every 36 hours which pretty much assures that.
As far as checking traps from a distance, I feel that is difficult with muskrat traps because they are usually set under water. There are exceptions, but for the most part... under water ... and the animal drowns with leg hold, or in the case of a conibear... a little bit more quickly.
But it isn't impossible. Since the trap was obviously a leg hold, it was likely set, just barely under water where muskrat enter and leave the water. It was likely set in such a way that the muskrat could instinctually head to deeper water and drown. It would be easy to check that set from a distance, provided the visibility in that water is more than a couple inches.
I wasn't there, but it seems to me that a trapper could EASILY check that trap from the other side of the creek, using binoculars. It's how I would have checked it. Trap still there? OK, checked. Nothing in it. Trap not there? Something in it.
There is NO WAY that duck was in that trap very long, or it would have drown. The trap likely weighed nearly as much as the duck. He would have tired out rather quickly and drown. Any other assumption, including that it was not being checked is based on emotion and LIKELY false IMO and wouldn't have saved that duck. I'm actually surprised it didn't drown in the time you took to take the pictures.
Chit happens. It was unfortunate. Mo matter how careful you are, other things can be caught.
When I trapped muskrats, I used mostly conibears because it almost completely eliminates the chance of catching a duck or another animal, and the animal dies quickly.
A couple years ago I played a practical joke on a guy and his son who I allowed to trap muskrats in my pond.
Anyway, After checking their traps, he comes up to me shaking his head with a weird smile on his face... "You will never believe this! Somehow, a possum got it's tail caught in one of the muskrat traps and then drowned itself!"
I couldn't keep from laughing because I put it there. Don't worry, it was dead before I put it there.
BTW, bluebirds eat a lot of bugs. I doubt it was there for grubs or worms.