I didn't realize I wanted this until I started playing Aurora 4x, but I really wish we had a turn-based space 4x that actually followed at least a pop-science understanding of relativity. Even something as simple as speed-of-light lag on communication would be a dramatic difference from normal 4X titles, to say nothing of the absence of FTL.
As a practical matter, the galaxy would probably have all its objects move mostly on rails until the player perturbed them and then rely on patched conics, but even under those conditions, I think it would be fun to play in space as boring and lethal as reality.
I have thought about this on and off, since about the time Master of Orion 1 came out. The problem is that the concept is cool, however the game probably wouldn't be. If a turn is 1 year, and say that a probe can travel at 0.5c, then to send your first probe to Alpha Centauri would take 8 turns, you'd find out about what it found on turn 12, then you could send orders to advance to the next star system, which would take 4 turns to be received (turn 16), and another 4 turns to acknowledge the orders were received (turn 20). Then, it would take 8 turns for said probe to move onto the next star system (turn 24) and you'd hear about
that on turn 32. So far, this isn't too big a problem. However, the real problems start to come when you are sending out ships that are supposed to be crewed by sentient beings. Unlike a probe, it makes no sense for a ship of humans to arrive somewhere, radio to base 50ly away and await a response for 100 years before deciding to do anything.
Other disconnects will creep in such as technology levels. Are outlying colonies going to have the old tech, and wait for new tech to be radioed-in from your home colony? What if the new colony ends up bigger than the capital, are they just going to put all R&D on pause while waiting for a distant start system to radio them with new tech updates? The problem is, this doesn't make sense either, so you need each group of sublight humans effectively doing their own R&D and ship redesigns, production, tactical and strategic planning, and not waiting around for "orders". The problem is that now, you must either have an entirely AI-driven "game" that almost entirely plays itself (which would be taking a more realistic approach), and it's not a 4X empire game after all, or you have a 4X god game with sublight communications where everyone except you is a dumbass who sits around twiddling their thumbs for decades while awaiting orders (which would be taking the straight forward "4x with sublight communications" approach).
Think: 4X is Star Trek or Star Wars, and if you add the sublight constraint, you've got Firefly or Cowboy BeBop instead. A different type of thing.