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.
Today’s date is March 1,697 2020.