They have shallow roots. When I bought this house there was a big old willow in my back yard. One wet summer a wind storm blew it down. It turned out the roots didn’t go very deep at all.
My memory of digging up ours is of a very solid taproot going down a long way, and lots of lateral roots, not deep, but capable of reaching pipes and structures a long way away. For a tree naturally found on riverbanks, this would give a combination of stability when the ground is waterlogged, and a water source in dry spells.
I would say go for it if you really want it! But there are lots of plants that like to get their feet wet without all the trouble. I am a fan of dogwood shrubs, Cornus stolonifera, has red twigs that are gorgeous in winter it gets covered in tiny white blooms all summer and produces berries. Highbush cranberry and Redbud are also good specimans for damp areas.
There are also perennials that would enjoy a streamside location, check your state’s DNR website for native species.