I think you could please everyone by including lots of options during game creation. Enable/disable timed quests, static or random galaxy, set the size, number of planets etc etc. You could make every game unique while keeping the central theme or plot static or even randomize parts of the main story.
An example would be (using SC2) that the Ilwrath-Pkunk war could be randomized so that theres a big conflict in the galaxy, but the alien opponents are random and the location could be random. Even the timing could be random, maybe you start a game and the war is nearing a conclusion, maybe it's just getting fired up or maybe there's a cold war situation going on and it goes hot while you're playing.
Replayablility would be nice. The timers in SC2 weren't great, but they did give you some incentive to try replaying the game (only once or twice, though), to try for different outcomes at things you failed before.
In terms of very randomized scenarios and content, they work well in sandboxes, but things like that are probably difficult to implement in a very story and dialogue heavy game. Random or semi-random star placement to make the map a little bit different each time could work.
Maybe you could use timers influenced by various in-game factors to show shifts and changes in a war, but not have them tied to game ending states. So while you could see the situation in the Ilwrath-Pkunk war progressively getting worse without your intervention (say, by showing the Pkunk territory changing/shrinking), the game would wait with the issue of final defeat/resolution until the player got actively involved. In that way we could have timers making success more difficult with time (Pkunk pushed back to a single holdout world), but not putting the player out of the loop or going "You're late? Ooops, it's all over now, sorry."
If you haven't met/discovered the aliens involved yet you could hear news from travelers or rumours of something brewing on the other side of the galaxy.
Haha, yeah, all manner of news and rumors are a must. Guess no Melnorme merchants to sell them for poor abducted critters this time around, though.
Edit:
Perhaps a compromise between the two... every in-game event is completable without requiring reloads/replays (as I believe has been mentioned already), and the player themself will instantiate the events initially (or at least be notified that the event is taking place), however some have built in failure conditions if the player does not action them within a certain amount of time? That way, the player (once notified of the event) has the choice of playing each particular event or sitting out of them and seeing where things go from there. Also, the player has the ability to fail something through inaction, giving a sense of urgency which the "everything on hold" method utterly fails to provide.
This should stop the annoyance of having missed an event through just not being in the right place at the right time, but still keep the feeling of urgency to act which keeps the player engaged in what is happening.
I actually like your compromise more than the one I proposed above. I don't mind fail states (I love well written fail states). However, these days doing anything that leads the player into a fail state sadly tends to be unpopular.