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Same reason you coat a treated wood deck. Makes it look better and lasts longer.
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I've got a flatbed that I made sideboards for and I decided that they would look better if they were black like the bed... wrong!
I used semi-transparent stain instead of paint as I thought it would soak in a bit and not show scuffs, scratches and shallow gouges but after a couple of years there were bare spots all over.
I re-stained them a time or two but it's really kind of pointless as it's a working truck and not a show truck. Should have left them bare .
As far as lasting longer if it's good quality treated wood (and there's different grades or levels/kinds of treatment) it will probably outlast all of us.
My deer towers I built with treated wood that I bought from a yard that caters to pole barn builders... my oldest one is around 15 years old and is as sound as the day I finished it.
Just my $.02. It's your trailer to do with what ever you want.