the use of Bayesian belief updating with expected utility maximization may be just an approximation that is only relevant in special situations which meet certain independence assumptions around the agent's actions.

— Steve Rayhawk

For those who aren't sure of the need for an updateless decision theory, the paper Revisiting Savage in a conditional world by Paolo Ghirardato might help convince you. (Although that's probably not the intention of the author!) The paper gives a set of 7 axioms, based on Savage's axioms, which is necessary and sufficient for an agent's preferences in a dynamic decision problem to be represented as expected utility maximization with Bayesian belief updating. This helps us see in exactly which situations Bayesian updating works and why. (In many other axiomatizations of decision theory, the updating part is left out, and only expected utility maximization is derived in a static setting.)