I think where I am at least, a liner would be worth it for the amount of water it keeps in the soil. My unlined/unsealed wood beds are a bleep to keep hydrated enough for plants in the summer.That's an interesting thought. I know that without lining, the wet soil will be directly in contact with the wood. If I put a barrier between the soil and the wood, that direct contact would be broken. But would you trap moisture against the wood? I don't know.
Here is a guy who sells raised bed liners, claiming that they preserve the wood longer...
But then I found this article on Should You Line A Raised Garden Bed? (4 Things You Need To Know) which states that a raised bed liner will cause the wood to rot faster - which answers your question affirmatively.
View attachment 3759424
Maybe where you live has the greater effect on the benefits of using a raised bed liner, or not. Where I live in northern Minnesota, it's the opposite of hot and humid. Having said that, I have never lined any of my wooden raised beds and they are still rot free after 5+ years. Using untreated pallet wood, I can expect 3-5 years of rot free service according to the sources I have found. In my backyard, the oldest pallet wood raised beds are going on year 4 and have no signs of rot.
One of the advantages to building your own pallet wood raised beds is that you know how to repair it if/when a board rots out. Here is a picture of one of my pallet wood raised beds v2.0 up on some sawhorses in process of being built...
View attachment 3759426
You can see how the pallet planks are on the inside of the 2X4 outer framing. The main advantage in that design is that the soil will be pushing outwards against the planks, into the stronger 2X4's, and I should never see any sidewall blowouts as many people have discovered if they put the planks on the outside of the 2X4 framing.
If a pallet plank rots out, I can simply remove that piece and put in a new one, or if not too badly rotted out, I could maybe just slip another pallet plank piece inside the original which would never show looking from the outside.
Frankly, these pallet wood raised beds v2.0 are holding up much better than I had hoped. My current plan is to use them until they fall apart and just replace the whole raised bed at that time. It costs me less than $2.00 to build each one of these raised beds and I can build one in less than an hour.
Getting back to your concern about lining the small planter with a chicken feed bag and would that just cause the wood to rot faster... I think I won't line the planters after looking into this issue. Thank you for asking that question. Again, these small planters take me less than half an hour to build and cost practically nothing out of pocket for me, so why put a liner in them when they might only cause the wood to rot faster? Probably not worth it.