Yes, I use mine all the time with just the velcro. I put all my shoes and misc. things that I want quick access to. Never had a problem with it staying.
I was surprised to hear others used bungies, It never occured to me that I would need them.
I'm in the middle of building a Harbour Freight trailer, I bought a large diamond plate truck toolbox from JCwhitney. Ordered LED trailer lights to reduce load on the electrical system.
But for around $500 you can build one.
Alot of people have gone this route and after looking at the trailer it appears to be very safe to me.