The fact that real-time can have a player get caught off guard is not particularly a bad thing. Surprise attacks are realistic. It also forces the player to make priorities and focus on the situation, which is also realistic. For some reason, monarchs tended to neglect infrastructure when they were at war.
However, for a real-time strategy to work, it has to avoid the tedium, especially if it is unnecessary, and to provide lots of quick information for timely decision making. As far as I can tell, EU does a good job of this.
For a counter example, 'Star Wars: Rebellion' (called 'Supremacy' in Europe, I believe) is how not to make a real-time strategy game. Unbelieveably simple but important tasks that could have easily been automated took up inordinate amounts of time compared to the interesting events. For example, the game forced the player to re-deploy spies after every mission, even if the unit was constantly repeating the exact same mission - a simple 'repeat mission' toggle could greatly have reduced the effort. The computer 'governors' were poor and totally unreliable so the player had to do everything. And the information systems made it difficult to find out anything important, especially the email-like message system that forced the player to open every message to learn info that could have been easily included in the subject (not to mention that incoming enemy fleets were not noteworthy enough to consider an alert). All this (plus a number of other serious flaws) made the game less of a game and more of a chore.
