This doesn’t make sense.
I presume it’s because getting up to your shins in mud makes it hard to draw your leg back out, whereas on stilts all your muscles and joints are above the stilt platform, allowing you to use them freely to draw the stilts out of troublesome terrain. That’s just a guess though.
Yes, and the thinness and smoothness of the stilts allows them to slide easily out of muck whereas legs with boots and clothes on them get stuck rather easily!
Doesn’t it also allow them to slide deeper in the muck than feet ever would? I’d think it would be better to wear something like snowshoes, yet here I am, looking at the picture and wondering.
I work in a salt marshes and traverse mud flats regularly, your take is correct, stilts could slide too deep and be exceedingly difficult to retrieve. This is a general statement YMMV (your marsh may vary) Stilts could potentially sink so deep as to exceed the legs range of motion and be impossible to extract, especially if both stilts sink in. Look at the feet of birds who live in marshes, they have oversized feet (like, as you said, snowshoes) to stay on top, avoid sinking in. Stilts advantage would allow seeing further in flat terrain.
It is not really to cross marshy ground but more to spot it and avoid it.
It also helps to keep an eye on all the sheep despite all the tall grass around them.
I haven’t seen this mentioned enough. If you’re job is to move and protect your flock then being high up and able to see further helps a lot.