Never done this on a bike trailer, but my wife and I have driven multiple thousands of miles with a couple 30-ish gallon totes strapped into a hitch mount basket on her little Kia Soul.
For my money, i prefer the 27 gallon tough totes from home depot since they are more square sided (better space utilization) and seem sturdier in compression (good for stacking or tying down with a ratchet strap)
If I was going to do that long term or with anything valuable inside, I might look into DIYing some weatherstripping around the rim to help keep water from getting inside.
Those look way more purpose built with tie down groves and shape. Thanks for mentioning them!
Not looking to tour or anything with the trailer, but if i had to do a major haul or XYZ, i was thinking a large enclosed container would be better than trying to hold everything together with cargo nets. LOL