But why would there be less automation in the future without some kind of setting Macguffin to handwave it like BSG had?
Because automation takes time, money and experience. You can automate a task after the task itself has been studied to death and you've had a couple of years to get an engineer to develop a whole system to make that task less labor and time intensive. That comes after YEARS of organizational experience, once your people have been doing these tasks so long and so often that you know exactly what can be automated and what can be done manually to make things easier.
Starfleet is not that organization. They've never flown into deep space before, they haven't completely figured out how everything should work. They know what they need to do, but the expertise for exactly HOW it should be done is in the heads of a few very smart people who need to be on their ship in order to do their jobs, and even those very smart people have almost no FIELD EXPERIENCE to make their jobs easier. Two decades from now, some of those bridge officers might come back and teach the next generation of Starfleet officers how to do their jobs, and they, in turn, will start talking with engineers saying "You know what would be cool? If we didn't have to physically pick up the phaser power cells and load them into their cradles by hand. We should have, like, a winch or a conveyor or something that can do that when you push a button."
And before you ask "Why didn't we have that in the first place?" It's because Enterprise was designed by a completely different group of people who designed the phaser banks; it's because the people who designed the armory are naval architects trying their hand at spaceship design for the first time and have NO IDEA what works and what doesn't work. It's because the people who designed the phaser banks have never worked on an active starship before and it never occurred to them that the power cells would have to be swapped every time the ship goes to battle stations (instead of, say, once a week or once a month).
Because knowledge isn't something you can just pull out of your ass because the script says you should know. Knowledge comes from experience, and 22nd century Starfleet doesn't have any.
I mean, we do have technology to do things for us. Today. That's a thing that's already happening, and automation has only been getting more and more prevalent. Saying that Enterprise should be like a modern day naval warship is like saying that a show set on a modern day naval warship should show it like an ironclad.
Except that modern day warships got the way they are through trial and error over 50+ years of development. The first guided missile cruisers, for example, had this amazingly complex load system where crewmen had to attach the warhead to the booster, then attach the fins, then attach the guidance system, then load the missile onto a rail to be loaded to the launcher. 20 years later they had the Mk-26 launcher with missiles that were basically pre-assembled, but still loaded (and maintained) manually before being positioned on the launch arms... and then one day someone said "Why do we even use a twin-armed launcher? Why not just fire them right out of the tubes?" and then VLS was born.
It took 30 years of trial and error for them to make that leap, and the automation systems that made that possible took at least as long. And this for a military that has effectively unlimited funding and unlimited resources to play around with shit like that. Starfleet in the 22nd century is so badly funded that the Vulcans can shut down entire exploration programs just by THREATENING to pull their support.