So 66 pages deep, thought I would finally jump in with my short list. Overall, 5e is a pretty good system, "everyone's 2nd favorite" as they say. So I think any attempts to "go radical" or likely to be met with failure. So we need to look at some key areas.
Monster Design
While the player side of the fence looks pretty good, the monster design I think is the biggest part of the system ripe for innovation. 5e monsters aren't very exciting especially when you compare it to 4e's monsters imo (4e monster design at least later on was some of the best imo).
This is the place that you could do the most overhauling. Players will still have their more traditional comfortable classes they know and love, without having to learn too many rules. The DM can take this one on to gain a new class of better monsters for more interesting encounters.
A few notes here:
1) Legendary Resistance "works" at stopping high level spells from one-shotting boss monsters but in the most boring way possible. A5e made some nice improvements here, but this is an area that we go more radical.
2) Vulnerability: Its too all or nothing in 5e, which is why its seen so rarely. Toning this down and bringing it back in gives us a lot of new options to play with.
3) Another look at legendary monsters. 4e's later solo monsters I think finally got to the sweet spot of what boss monsters should look like. We have also had some really innovative stuff on the 3pp side that could be incorporated here. Legendaries in 5e are ok but they still don't do the proper job.
Concentration
I do think WOTC inclusion of this mechanic is good. It helps to trim down so much of the bloat of buffs that was the hallmark of mid to high level 3e play especially. But...the mechanic is TOO restrictive.
The problem is the mechanic tries to solve two problems at once.
1) We want to ensure certain buffs are not stacked on top of each other.
2) We want an interruption mechanic so that certain powerful spells can be "stopped" through damage or other effects.
Both of these are excellent things to model....but they are two completely different things, and should have two mechanics. Having a summon spell that my fighter can interrupt is great. Having a defensive spell that can't be stacked with 5 other defensive spells is wonderful. Having a defensive buff that can go down at the first hit is not good.
So splitting concentration into two separate things would solve a lot of the constriction with concentration.
20 10 levels
We have had 20 level dnd for a while now (though not always). And the data is in....people don't play 20 level dnd. Study after study has consistently shown that campaigns that make it to 20 levels are unicorns. 10 is the highest many people ever play, and sometimes not even that high. (and I am saying this as a DM who has gone to 20th level, even 25 in 4e once before).
And yet the conversations around high levels often consume so much of the design discussion oxygen. Many many discussions on these very boards amount to "this breaks at high levels". It is not productive to have so much design space dedicated to an area your audience does not use.
Its time to toss 11-20 level dnd into the trash, and go back to the name level concept. At 10th level (maybe 11th), you are at the peak, and you normally retire. And then for those players that want to keep going, you introduce your "epic feats" or "epic bonuses" or "epic rituals" to lay on top....so you can still bring in those classic high level spells and effects into the narrative....but in a small portion of the design space.
Heck, 10th level parties in 5e can already take on adult dragons, they are already hitting the pay grades you need for most big world ending type stories.
Every once in a while someone comes in and says they want a 30 level or even a 50 level dnd, and everyone kind of laughs and goes "well maybe they will make an epic level book for that or something", but no one takes it too seriously. Well its time for the 11-20 level players to take that as well....put 11-20th in some kind of immortals/epic handbook, and craft a 10 level system that is tight, fun, and chock full of awesome....instead of stretching it over a level range a small fraction of your audience will ever see.