There are a few implications but most of them are just aggravating already existing factors.
1. Positioning will become even more relevant.
Positioning is already relevant but when a fall causes even more damage some risky places become deadly places. The fall from the top of a 40ft. rampart that caused 4d6 now causes 10d6 damage, what could hurt your character after a shove now can kill him. Every edge from a high place becomes even more important to not get close to it or more rewarding to use offensively.
2. Feather Fall just became more necessary.
Feather Fall already is one of those spells that you always want to have because you never know. A 6th level wizard that was just worried to be throw down 60ft after flying now should be terrified of the idea; he might survive 6d6 but hardly would upon receiving 20d6 damage.
3. People that can avoid falling damage got comparatively more mobility.
You're chasing a 4th level bard and he jumps of a 50ft building, cast Feather Fall and safely reaches the ground. A Fighter or Barbarian might be able shrug 5d6 and keep the chase but even a monk with Slow Fall would think twice in jumping down when the damage is 15d6, ignoring 20 damage, the average of 15d6 still would result in 32,5 damage. The same monk could jump into an existing ledge 10ft under and then to the ground and probably get off with 15 damage, but his companions can't easily follow unless they slowly climb down or have the similar resources.
4. Athletics and Acrobatics became even better skills.
They still aren't Perception, but one of them reduce falling damage and the other helps you to climb up or down and not fall. When falling damage just got lethal, not receiving it becomes more important than before, raising the value of those skills.
5. Spells that can throw you instead of direct damage got a lot more lethal.
Telekinesis, Reverse Gravity and Bigby's Hand can kill a lot more effectively to the point of being almost broken since they can continuously cause 20d6 with a single spell. Beware of those.
6. Knocking flying creatures prone becomes more lethal.
Any ability that knocks someone prone becomes far more lethal since non hovering flyers will fall as a result and take much more damage. (@OganM's point).