Sorry…missed this before. I haven’t had many issues with my white willow, but I agree with tamarack that it loves to drop small branches…especially late winter into early spring. If the area is far enough from your well, septic, sewer, and/or foundation it’ll probably be fine. Agree with tamarack about red maple. Other options would be river birch or bald cypress. I’m a fan in bald cypress in swampy areas.
Does the area retain water only during wet periods for a few days or is it semipermanent? I have an area where I grow my pawpaws that will rarely pond up, but it drains within 24-72 hours. Those fruit trees can tolerate that since they’re native to river plains that occasionally flood. But anything more than a few days for those trees will start to damage them.