I want to see a space 4x that takes the best (for my tastes anyway) features of all the existing space 4x games, expands on some of them, and combines them into one game.
Key features:
An extensive, deep, and above all interesting research tree. I don't want to be just unlocking bonuses to things, I want to be unlocking the ability to do things I couldn't before, or do things in a new way. Lots of different ship components giving new abilities, different weapons and defenses with their own strengths and weaknesses - but not a simplified rock/paper/scissors system. Ideally this would also involve either randomized tech trees and/or some sort of choice system, such that each game you'll be doing things in a different way. Sword of the Stars is probably the closest to what I'm looking for in this regard, although I'd want a tech tree a good 2 to 3 times the size of the one in that series. There's a few examples of exactly what I don't want - GalCiv is the one that springs to mind though.
Fully designable ships, as freeform as possible. Avoiding hard coded ship sizes and layouts, make it more about what you can afford to build and maintain. Aurora is probably the best existing game in that regard. To be honest I don't mind if it's a little more restricted - I'm happy with games like Space Empires or Distant Worlds in that regard, but since this is the ideal wish-it-existed game fully freeform is my ideal.
Customizable races. This is something most 4x's do a decent job of, so I won't expand on this.
I'm not sure if I'd prefer turn based or real time combat, but the player needs to have the option for full control of their ships. I think ideally I'd like the player to have 3 choices: 1) straightforward instant autoresolve, 2) issue general orders (akin to e.g. Gratuitous Space Battles) and then watch the battle, 3) full control. Also, smaller ships should still have a role in battle in the mid to late game, e.g. by using a speed vs tracking system similar to Eve or Aurora.
When it comes to empire management, I'm a little less sure of exactly what I want. I think Distant Worlds is probably my favourite here though - I get a feeling of a proper empire in that game, and for the most part the AI automation works really well, keeping me from having to micromanage too much but letting me do so if I want. But I'd maybe want to see more world development than DW has, in terms of planetary improvements, trade worlds, and such. Also plenty of random planetary/system features that may prompt a planet being specialised for a particular purpose, and just to make exploring a bit more interesting.
Nostalgia may be colouring my memory here, but I remember Imperium Galactica having a fairly neat take on random events, where they were more like micro story arcs, and you actually had to go out and do do something to deal with or benefit from it, rather than just be informed that you're getting bonus/penalty X for Y turns. And if even if I am misremembering, I still want something like that.
AI's and diplomacy and such - I don't have a lot to say on this other than I don't want the AI to be obviously cheating, and I don't want them to be treating the player any differently than they treat each other. And ideally they're not totally erratic and random, making stupid demands when they're in no position to do so, or turning down deals that will clearly benefit them without a good reason. Ideally it would all feel like an actual simulation of galactic empires, a sandbox universe where they all have their own agendas and politics beyond just "beat the player".
Graphics - while I don't need fancy graphics for a good game (I'm perfectly happy with Aurora's spreadsheets and text logs), I do get a lot of satisfaction from watching the light show of a newly designed battleship unload its newly researched plasma cannons on the enemy, so my ideal game would have plenty of shiny in that regard.
I've gone on a bit now, so while there's other areas of gameplay I've not touched on I'll wrap up there by saying I want a 4x that feels properly epic, and which gives me lots of complexity, depth, and choices through every aspect of the game. It may well be that in practice it'd be a horrible tangled mess, but in most cases these are things that existing games have done a decent job in one or two areas, but none that I can think of manage to get it all in one game, so I'm always kinda disappointed.