So not having any precision rifle experience, I've been wondering.

Assuming you have a typical bolt action rifle, with a fully freefloated barrel which only contacts the receiver/action where it's threaded in, and the receiver then sits in the stock. How does bedding the receiver and stock improve accuracy? Your barrel never touches the stock so the stock should have no effect on its harmonics or warp when heating up. Your sights would typically be a scope mounted to the receiver or iron sights mounted to the barrel or barrel and receiver. Either way the only variable there is the interface between barrel and receiver. The stock should have no impact on it. So as long as your sight-receiver-barrel interface stays consistent, how does some minor play in the stock impact any of it?

Bedding eliminates misalignment between receiver and stock interface angles. Epoxy based compounds makes it easy, machined blocks and chassis are much more solid but improvements to accuracy will usually be undetectable. Epoxy bedding and a torque wrench on the action screws will get 99% of possible improvement.

Variance in recoil during barrel time.

Consistency.

The action will move a small amount in the stock under recoil in an unbedded action. The bedding improves the fit of the action into the stock and reduces any minor movement.