Even though the Imperium might be a thinly disguised dictatorship, they can't control the news enough to prevent word from getting out that capital ships haven't been seen in a large number of systems in decades. Free traders, passengers, etc, will all carry that news. In order to maintain power, reassure it's member worlds and allies, and appease it's nobles, the Imperium simply must parade it's fleets around - even if the bulk of the population will only see the ships on holovid. Sure, a destroyer or three may swing through a system every 2-3 weeks, but that won't capture the local's attention and make them feel cared for like a task force every couple of years will.
Militarily, not really needed. Politics, Diplomacy and Economics are what would drive those fleets.
A ship may be a 100% artificial environment and quite controllable, but there are still subtleties that a true crisis presents that a human will pick up on. FREX, jump sickness caused by the transition to real space. I seriously doubt even the super sophisticated computers and systems of the Imperium could duplicate that effect on their crewmen reliably. Which means at a minimum, taking those ships into j-space so that a simulation can be run at the moment they drop out.
More reasons for live-fire exercises - ammo sampling, equipment reliability testing and data collection.
If you never fire off any of your ammo, you don't know for a fact that it all works. If a saboteur comes through and scrambles the proximity fuse programming for your missiles or a large portion of the warheads have experienced undectable damage from a radiation event, you may only discover it when you fire the missiles for real. Most militaries would rather catch that type of problem during a live fire exercise than find out during hostilities.
Anything with moving parts needs to be tested under stress periodically. A live fire exercise is a good way to make sure your mechnical parts for your sandcasters and missile launchers are all working.
Live fire exercises also provide provide opportunities to collect the data with which the simulations are programmed.
Point is, that even with superior simulations covering most training, there are still enough valid reasons that can be combined together to justify live fire exercises.