Whenever I put plants in a cardboard box, first I lay some plastic inside the box, draped so that runoff water can't get to the cardboard. You can even bottom-water a tray that way.
HD givves away shallow cardboard trays. With a plastic-bag liner, I reuse those for a few years.
BUT rain or over spray from watering still dissolves the boxes from the outside in. Milk crates sound much better!