The simplest and obvious observation on this story, is that it looks like damage output is currently too high compared to hit points, which clearly makes a fight last very short.
A second, more important observation, is that we should be careful when talking about SPEED of combat. We all wanted combats to run more smoothly, and 5e is quite good at that so far, meaning that the rules don't drag combat down, making you spend too much time counting bonuses, tracking status etc. That's great, but clearly is not enough to guarantee that combats will be exciting and memorable, this is just an obstacle for that which 5e is trying to remove or reduce.
LENGTH of combat can mean two things: how long does it take in absolute time, and how long does it take in number of turns. It's easy to imagine that a combat that takes 1 hour to resolve during which each player got 1 turn that took 15 minutes to resolve, would be very different than 1 hour during which there were 15 turns of 1 minute per character. I suppose that some balanced solution would hit a sweet spot... 1 hour for a fight against the BBEG could be a fairly reasonable upper bound (some gaming groups may not want more than half of that, however), but how should it be broken down in turns?
Furthermore, let's keep in mind that you can't just stretch a combat by increasing everybody's HP, at least not too much, because then characters who are strongly based on daily abilities would get progressively weaker than those who are based on at-wills.
Finally, I seriously hope that 5e resists the temptation of going with the wind of "everything is HP damage after all", because despite the good conceptual reasons for that, this idea carries the danger of turning a long combat into mere attrition, thus it goes against any attempt at making a battle vs BBEG more memorable just by making it longer... it also makes it tedious.
What could really be a solution here, I don't know. I can't even say how a combat should feel like to be memorable, it's easier to say how it shouldn't be. Certainly, a combat that is too short is hardly memorable (which can result also because of insta-kill, not just because of too high damage output). A combat that is spent more taking care of the rules rather than in-game decisions is not great fun except for those who actually like the math more than anything else in the game. A damage-HP drag without much tactics can make all fights feel similar.
Ultimately, I am afraid that we can only partially count on the system to help us with that, it will be very good already if it manages to avoid the problems above. But most likely, it will be always up to a good DM and good players to turn the fight into something memorable. And I actually think that the OP's example was pretty memorable... except that there were too few rounds, which means that at such high levels the current system definitely need some dialing.