(I don’t know why I wrote “initial purchase choices” when I meant “individual purchase choices”, but obviously it was comprehensible anyway.)
As for whether budgeting is ever a good idea when the amounts are small enough for utility to be close to linear—I think it does two useful things: it saves cognitive effort, and it may help you resist spending more than, on careful and sober reflection, you would want to. How often those are worth the utility-loss from using a cheap approximation will vary.
(I don’t know why I wrote “initial purchase choices” when I meant “individual purchase choices”, but obviously it was comprehensible anyway.)
As for whether budgeting is ever a good idea when the amounts are small enough for utility to be close to linear—I think it does two useful things: it saves cognitive effort, and it may help you resist spending more than, on careful and sober reflection, you would want to. How often those are worth the utility-loss from using a cheap approximation will vary.