I voted before looking at the defined frequencies, so my two "sometimes" votes for both time-related and dramatic deadlines should actually be closer to "rarely".
In the majority of my adventures, the PCs are not on any kind of deadline and may proceed at whatever pace they enjoy. Introducing a deadline of any kind thus allows me to mix up the pace a bit, and deliver different experiences at the table.
Time-related deadlines often constrain the number of times that the PCs can refresh resources (resting to regain spells/powers and recover hit points). Time-related deadlines can thus emphasize the more strategic elements of a game (should the PCs rest now, or can they risk one more fight?), and push the PCs to go as far as they can before they rest.
IMO, dramatic deadlines are only meaningful if they also impose a constraint. If the PCs arrive in the nick of time and proceed to take down the BBEG in an otherwise ordinary fight, you might as well have them arrive five minutes or even an hour earlier. Arriving in the nick of time should mean that something bad is going to happen unless the PCs stop it almost immediately. So, dramatic deadlines effectively become time-related deadlines too, but the deadline is measured in terms of rounds instead of hours or days. Dramatic deadlines used in this manner limit the number of actions that the PCs may take, and this emphasizes the more tactical elements of the game. The PCs have to ensure that each action that they take counts.