The two different types of adventures - event-based and location-based - both have time pressure built in. Event-based adventures have the villain's timeline. Fail to stop the villain's plans and bad things happen. Location-based adventures can have the risk of random encounters. This is discussed and recommended in the DMG. As such, this seems like the intended form of play to me.
Contrary to the belief of some, however, "doom clocks" can always be made to fit "narratively." Being a game of make-believe, the narrative is quite malleable in that way - you can just make it up! If the DM doesn't want to, it hardly seems appropriate to blame WotC for an undesirable result that comes up by not playing in the way that is intended.