It is proper to burn cards if there is no further action?
i.e. all in preflop, or after the flop
It is proper to burn cards if there is no further action?
Yes, absolutely. There is no case where it is not considered proper to burn cards if there is no further action.
Some Context: Cards are burned to prevent live cheating. There is no scenario where this should not be done.
Reason: Players can see the top card of a deck. If the next card has any physical marks that may help to identify it - without burning - players could know the following card. With burning, each card is completely unseen during action before that street.
For example,
i.e all in preflop
Someone could intentionally mark an Ace when they get it, see the ace is coming on the turn (by the marked top card) and shove on the flop to knowingly hit their ace on the turn.
I agree with @Danny in that the cards should always be burned. This should apply even in the case of all-in preflop, for 2 reasons:
while pre-flop, you can see the top card of the deck, so you might make a decision to do the all-in move you mentioned based on that information
it's a dangerous precedent to introduce exceptions to the rule (or any rule) because, after a while, you will end up with multiple such exceptions, which can only be detrimental to both the integrity of the game and its learning curve.