tldr; daily quests should be given out randomly instead of all players competing for a single area.
Dailies get harder to do when there are more people doing them as opposed to Battlegrounds or Dungeons or Raids purely due to competition. More people looking for groups creates its own solutions to any bottlenecks by creating more groups or battlegrounds for them to compete in, but there's only ever 1 zone a day that hosts the repeatable daily quests which also is competing against regular players who are leveling up.
Players could stockpile daily quests by accepting them and doing them at a later date, but this is a limited solution as the maximum quest log is 25 and the limit for daily quests tops out at 42.
Daily quests are grouped by geography into a portion of a single zone in Outland. Players could be randomly assigned one of the many groups of quests such that they'll be doing their dailies in one zone while other players are doing the same thing but elsewhere. This will reduce the amount of competition and player collisions by getting the players to not encounter each other by giving them different quests.
Congestion could be further reduced by adding in more areas for dailies in the old world. This could also be expanded to allow players who aren't max level to participate in those quests as well and gain experience as well as the other rewards. Max level players need to have those quests scale to 70, however, even if it's the old world.