Plastic and lumber grow beds might work but you may also wind up with some major leak issues.

I've had experience with people trying to line ponds with heavy builders plastic. Problem is that stuff gets little holes real easy and multiple layers doesn't fix the problem. It is a lot harder to replace the plastic in a gravel filled grow bed than it is to replace the plastic for a water filled hydroponics trough. The simple act of dumping the gravel into a plastic lined bed might tend to punch little holes in the plastic depending on the type of gravel involved.

However, if it is the only material available and if the set up is done so some small leaks won't really cause major issues, then perhaps it is still appropriate to use. Arrange things so that leaks might be directed to some dirt planting near the system that can utilize any leaking water to benefit and so long as good top up water is freely available then it might be ok.

Anyone who has read through my system thread on the other forum, will know that I have run into some major problems with my lumber and pond liner grow beds lately. And I have some heavy duty pond liner, the heavy EPDM stuff. Stands up great to gravel scraping it but unfortunately, anything that can eat wood can chew through the liner too. Termites and carpenter ants have caused me to switch to rubermaid stock tanks as grow beds.