Also a good question, and it may be that you're not the target if you already make heavy use of lots of different generator sites (do you ever use fantasynamegenerators.com?)
What I'm hoping will be useful is
- A generator that unites the most useful content in one place and with one click. It will provide enough to run a session with nothing prepared or provide enough to improv when players go on random tangents.
- Generators focused on content for 5E. I'd use O.G.R.E and reuse (or repurpose) several of the generators already available on the EN World
- Description-based summaries, giving content as a passage of text instead of a list of separate parts for an item. This Random Room generator shows best what I mean, where there is both the description and those bits split out into component parts.
I've just seen you're the author of Haunting of Calrow Ruins! Running that at the moment for my group on Roll20!
That's an ambitious goal. I suspect you'll run up against some built-in paradoxes...
(1) Randomly generated adventures (typically this means dungeons) are meant to spare a time-harried DM from prep / use in the moment when players go "off the beaten path"...however my experience has been that such random adventures take more prep work than adapting actual published adventures...I suspect this is because no generator I've seen makes connections between elements to the extent that a human being can.
(2) Focusing on 5e content means what? Focusing on 5e crunch (e.g. writing up traps "5e style" with 5e DCs/damage and using monsters in the 5e MM)? However, the strength of a generator has to do with the ideas it generates. No one can fully flesh out everything in a generator.
If there was a single one-click generator to help out 5E DMs with game/session prep, what should it include?
This would most likely for a time when you have nothing/little prepared, have players who go off on random tangents or have an idea and just want to run with it....
If I'm reading your original post correctly, you want to be able to generate the bones of an adventure with a single click. For that, you'd need...
Not really, that could be another generator though.
I want to give some elements which GMs often need during a game session which would be useful to have in many situations and can create easily in one place.
They might need something to fill a gap in an adventure, use a few things to spice up a journey, describe part of a city or have enough to run a short ad-hoc adventure for that game day.
I'm not focusing on trying to build an adventure.
I DM from a laptop behind a DM's screen. It would be nice to have all the info from the screen on my laptop, in addition to weapon/armor tables, magic items lists, etc.
I've tried to run with a laptop only when I have a pdf adventure (or on Roll20!) but I wonder if any research has been done on what proportion of people use a tablet or laptop when running a game at the table...
I've used this calendar tool at http://e2ogame.net/homepages/antti/rpg/gmtool.html before which has several things you can customise

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.