You need to bed any action into its stock, if the bedding is causing the rifle to shoot poorly and you want it to do better.
It doesn't sound like that's the case in your instance.
But it's certainly easier to bed the walnut stocks than it is the plastic ones, as the walnut ones are nice and rigid and don't have all the hollows that you would need to fill out. Pillars are nice but not always essential.
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